calculus

Question 1

1.  

Evaluate the integral.

		11
		-40
		16
		1

2 points  

Question 2

1.  

Find v ∙ u. v = 8i + 3j and u = 2i + 3j

		16i + 9j
		7
		25
		10i + 6j

2 points  

Question 3

1.  

Find the length and direction (when defined) of u × v. u = - 

i + 

C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q41g2.jpg

j + k, v = i + j + 2k

		2 C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q41g13.jpg ; -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q41g14.jpg i +  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q41g15.jpg j -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q41g16.jpg k
		2 C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q41g3.jpg ;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q41g4.jpg i +  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q41g5.jpg j -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q41g6.jpg k
		8;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q41g7.jpg i -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q41g8.jpg j -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q41g9.jpg k
		8;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q41g10.jpg i -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q41g11.jpg j +  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q41g12.jpg k

2 points  

Question 4

1.  

Find the general solution for the differential equation.

 = 15x2

		y = 15x3 + C
		y =  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q28g2.jpg  + C
		y = x3 + C
		y = 5x3 + C

2 points  

Question 5

1.  

Find fx, fy, and fz. f(x ,y, z) = sin (xy) cos (yz2)

		fx = y cos (xy) cos (yz2); fy = x cos (xy) cos (yz2) - z2 sin (xy) sin (yz2); fz = 2yz sin (xy) sin (yz2)
		fx = y cos (xy) cos (yz2); fy = z2 sin (xy) sin (yz2)- x cos (xy) cos (yz2); fz = 2yz sin (xy) sin (yz2)
		fx = y cos (xy) cos (yz2); fy = x cos (xy) cos (yz2); fz = -2yz sin (xy) sin (yz2)
		fx = y cos (xy) cos (yz2); fy = x cos (xy) cos (yz2) - z2 sin (xy) sin (yz2); fz = -2yz sin (xy) sin (yz2)

2 points  

Question 6

1.  

Find fx, fy, and fz. f(x, y, z) = x2y + y2z + xz2

		fx = 2xy; fy = x2 + 2yz; fz = y2 + 2xz
		fx = 2xy + z2; fy = x2 + 2yz; fz = y2 + 2xz
		fx = 2xy + z2; fy = x2 + yz; fz = y2 + xz
		fx = 2y + z2; fy = x2 + 2z; fz = y2 + 2x

2 points  

Question 7

1.  

Find the length and direction (when defined) of u × v. u = 5i + 3j , v = i - j

		8; -8k
		8; -k
		2; -2k
		2; 2k

2 points  

Question 8

1.  

Write the first four elements of the sequence.  

n

		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q45g13.jpg , -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q45g14.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q45g15.jpg , -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q45g16.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q45g5.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q45g6.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q45g7.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q45g8.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q45g9.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q45g10.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q45g11.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q45g12.jpg
		1,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q45g2.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q45g3.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q45g4.jpg

2 points  

Question 9

1.  

Find the general solution for the differential equation.

 = x - 15

		y =  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q29g3.jpg  - 15x + C
		y =  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q29g2.jpg  - x + C
		y = x3 - 15x + C
		y = 2x2 - 15 + C

2 points  

Question 10

1.  

Find the integral.

		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q47g4.jpg (2t + 5)4 + C
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q47g3.jpg (2t + 5)4 + C
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q47g5.jpg (2t + 5)4 + C
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q47g2.jpg (2t + 5)4 + C

2 points  

Question 11

1.  

Find the integral.

		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q49g4.jpg (6x - 7)3/2 + C
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q49g5.jpg (6x - 7)3/2 + C
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q49g2.jpg (6x - 7)3/2 + C
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q49g3.jpg (6x - 7)3/2 + C

2 points  

Question 12

1.  

Find the integral.

		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q48g4.jpg  + C
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q48g2.jpg  + C
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q48g3.jpg  + C
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q48g5.jpg  + C

2 points  

Question 13

1.  

Write the first four elements of the sequence.

		0,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q44g2.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q44g3.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q44g4.jpg
		0,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q44g12.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q44g13.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q44g14.jpg
		ln 2,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q44g5.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q44g6.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q44g7.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q44g8.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q44g9.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q44g10.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q44g11.jpg

2 points  

Question 14

1.  

Find fx, fy, and fz. f(x, y, z) = z(ex)y

		fx = zxexy; fy = zyexy; fz = exy
		fx = zyexy; fy = zxexy; fz = exy
		fx = zyexy; fy = zxexy; fz = zexy
		fx = zexy; fy = zexy; fz = exy

2 points  

Question 15

1.  

Evaluate the double integral over the given region.

 R = 

C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q8g2.jpg

		π
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q8g3.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q8g5.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q8g4.jpg

2 points  

Question 16

1.  

Find 

 and 

C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q13g2.jpg

. f(x, y) = (4x4y3 + 10)2

		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q13g7.jpg  = 16x3y3;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q13g8.jpg  = 12x4y2
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q13g3.jpg  = 2(4x4y3 + 10);  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q13g4.jpg  = 2(4x4y3 + 10)
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q13g5.jpg  = 24x4y2(4x4y3 + 10);  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q13g6.jpg  = 32x3y3(4x4y3 + 10)
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q13g9.jpg  = 32x3y3(4x4y3 + 10);  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q13g10.jpg  = 24x4y2(4x4y3 + 10)

2 points  

Question 17

1.  

Find the general solution for the differential equation.

 = 4e3x

		y = 12e3x + C
		y =  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q31g3.jpg e3x + C
		y =  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q31g2.jpg e3x + C
		y = 4e3x + C

2 points  

Question 18

1.  

Find the length and direction (when defined) of u × v. u = -3i - 8i - 4k, v = 0

		0; no direction
		0; -3i - 8i - 4k
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q42g2.jpg ;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q42g3.jpg (-3i - 8i - 4k)
		0;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q42g1.jpg (-3i - 8i - 4k)

2 points  

Question 19

1.  

Find the general solution for the differential equation.

  - 6x2 = 4

		y = -2x3 + 4x + C
		y = 2x3 + 4x + C
		y = 2x3 - 2x + C
		y = 2x3 + 2x + C

2 points  

Question 20

1.  

Find the angle between u and v in radians. u = 10i + 6j + 6k, v = 7i + 2j + 4k

		1.12
		0.23
		1.48
		1.34

2 points  

Question 21

1.  

Find the length and direction (when defined) of u × v. u = 2i + 2j - k, v = -i + k

		3;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q40g4.jpg i +  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q40g5.jpg j -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q40g6.jpg k
		9;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q40g10.jpg i -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q40g11.jpg j +  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q40g12.jpg k
		3;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q40g1.jpg i -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q40g2.jpg j +  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q40g3.jpg k
		9;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q40g7.jpg i +  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q40g8.jpg j -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q40g9.jpg k

2 points  

Question 22

1.  

Find the integral.

		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q50g8.jpg C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q50g9.jpg  + C
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q50g4.jpg C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q50g5.jpg  + C
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q50g2.jpg C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q50g3.jpg  + C
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q50g6.jpg C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q50g7.jpg  + C

2 points  

Question 23

1.  

Find 

 and 

C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q20g2.jpg

. f(x, y) = x3 + 9x2y + 2xy3

		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q20g9.jpg  = 3x2;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q20g10.jpg  = 9x2 + 6xy2
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q20g3.jpg  = x2 + 9xy + 2y3;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q20g4.jpg  = 9x2 + 2xy2
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q20g7.jpg  = 3x2 + 2xy + 2y3;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q20g8.jpg  = 9x2 + 3xy2
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q20g5.jpg  = 3x2 + 18xy + 2y3;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q20g6.jpg  = 9x2 + 6xy2

2 points  

Question 24

1.  

Evaluate the double integral over the given region.

 R = {(x, y): 1 ≤ x ≤ 8, 7 ≤ y ≤ 9}

		1008
		504
		672
		336

2 points  

Question 25

1.  

Evaluate the integral.

		1080
		4320
		- 5400
		- 2880

2 points  

Question 26

1.  

Find 

 and 

C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q12g2.jpg

. f(x, y) = 10x - 4y2 - 2

		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q12g7.jpg  = 8;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q12g8.jpg  = -8y - 2
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q12g9.jpg  = 10;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q12g10.jpg  = -8y
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q12g5.jpg  = -8y;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q12g6.jpg  = 10
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q12g3.jpg  = 10x;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q12g4.jpg  = -8y

2 points  

Question 27

1.  

Find fx, fy, and fz. f(x, y, z) = ln (xy)z

		fx =  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q23g3.jpg ; fy =  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q23g4.jpg ; fz = ln (xy)
		fx = -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q23g7.jpg ; fy = -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q23g8.jpg ; fz = ln (xy)
		fx = z ln  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q23g1.jpg ; fy = z ln  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q23g2.jpg ; fz = ln (xy)
		fx =  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q23g5.jpg ; fy =  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q23g6.jpg ; fz = z ln (xy)z - 1

2 points  

Question 28

1.  

Evaluate the double integral over the given region.

 R = {(x, y): 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}

		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q10g5.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q10g3.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q10g4.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q10g2.jpg

2 points  

Question 29

1.  

Evaluate the double integral over the given region.

 R = {(x, y): 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}

		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q9g2.jpg (e5 - e3 - e2 - 1)
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q9g4.jpg (e5 - e3 - e2 + 1)
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q9g3.jpg (e5 - e3 - e2 - 1)
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q9g5.jpg (e5 - e3 - e2 + 1)

2 points  

Question 30

1.  

Find 

 and 

C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q14g2.jpg

. f(x, y) = 

C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q14g3.jpg

		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q14g12.jpg  = -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q14g13.jpg  ;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q14g14.jpg  =  -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q14g15.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q14g16.jpg  = -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q14g17.jpg  ;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q14g18.jpg  =  -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q14g19.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q14g4.jpg  =  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q14g5.jpg  ;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q14g6.jpg  =   C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q14g7.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q14g8.jpg  = -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q14g9.jpg  ;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q14g10.jpg  =  -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q14g11.jpg

2 points  

Question 31

1.  

Find 

 and 

C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q16g2.jpg

. f(x, y) = sin2 (2xy2 - y)

		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q16g9.jpg  = 4y2sin (2xy2 - y) cos (2xy2 - y);  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q16g10.jpg  = (8xy - 2) sin (2xy2 - y) cos (2xy2 - y)
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q16g3.jpg  = 2sin (2xy2 - y) cos (2xy2 - y);  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q16g4.jpg  = 2sin(2xy2 - y) cos(2xy2 - y)
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q16g5.jpg  = 4y2sin (2xy2 - y) cos (2xy2 - y);  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q16g6.jpg  = 2sin (2xy2 - y) cos (2xy2 - y)
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q16g7.jpg  = 2sin (2xy2 - y) cos (2xy2 - y);  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q16g8.jpg  = (8x - 2) sin (2xy2 - y) cos (2xy2 - y)

2 points  

Question 32

1.  

Find the angle between u and v in radians. u = 8i - 7j - 3k, v = 4i + 3j - 7k

		1.23
		1.57
		1.41
		0.34

2 points  

Question 33

1.  

Find the integral.

		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q46g4.jpg (2x + 5)4 + C
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q46g2.jpg (2x + 5)4 + C
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q46g3.jpg (2x + 5)4 + C
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q46g5.jpg (2x + 5)4 + C

2 points  

Question 34

1.  

Evaluate the integral.

		-  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q5g3.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q5g5.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q5g2.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q5g4.jpg

2 points  

Question 35

1.  

Find 

 and 

C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q15g2.jpg

. f(x, y) = ln 

C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q15g3.jpg

		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q15g12.jpg  =  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q15g13.jpg ;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q15g14.jpg  =  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q15g15.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q15g16.jpg  = -ln  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q15g17.jpg  ;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q15g18.jpg  = ln  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q15g19.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q15g8.jpg  = -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q15g9.jpg ;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q15g10.jpg  =  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q15g11.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q15g4.jpg  = -ln C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q15g5.jpg  ;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q15g6.jpg  = ln  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q15g7.jpg

2 points  

Question 36

1.  

Find the length and direction (when defined) of u × v. u = 4i + 2j + 8k, v = -i - 2j - 2k

		6 C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q39g3.jpg ;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q39g4.jpg i +  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q39g5.jpg k
		180;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q39g6.jpg i +   C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q39g7.jpg j +  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q39g8.jpg k
		6 C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q39g9.jpg ;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q39g10.jpg i -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q39g11.jpg k
		180;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q39g1.jpg i +  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q39g2.jpg k

2 points  

Question 37

1.  

Write the first four elements of the sequence.

		-1, 1,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q43g2.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q43g3.jpg
		1,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q43g4.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q43g5.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q43g6.jpg
		0,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q43g11.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q43g12.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q43g13.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q43g7.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q43g8.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q43g9.jpg ,  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q43g10.jpg

2 points  

Question 38

1.  

Evaluate the integral.

		60
		8
		120
		4

2 points  

Question 39

1.  

Evaluate the double integral over the given region.

 R = {(x, y): 0 ≤ x ≤ π, 0 ≤ y ≤ 1}

		9π - 9
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q11g2.jpg
		π
		9π

2 points  

Question 40

1.  

Find the angle between u and v in radians. u = -4i + 10j - 6k, v = 10i + 7j - 9k

		1.10
		1.57
		1.35
		0.47

2 points  

Question 41

1.  

Find v ∙ u. v = -5i + 4j and u = 7i + 3j

		-23
		2i + 7j
		-47
		-35i + 12j

2 points  

Question 42

1.  

Evaluate the integral.

		77
		- 539
		847
		- 847

2 points  

Question 43

1.  

Find 

 and 

C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q17g2.jpg

. f(x, y) = ln yx

		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q17g12.jpg  = ln y;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q17g13.jpg  =  - xln y
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q17g6.jpg  = xln y;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q17g7.jpg  = -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q17g8.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q17g3.jpg  = 0;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q17g4.jpg  =  -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q17g5.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q17g9.jpg  = ln y;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q17g10.jpg  =   C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q17g11.jpg

2 points  

Question 44

1.  

Find 

 and 

C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q19g2.jpg

. f(x, y) = xye-y

		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q19g3.jpg  = ye-y;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q19g4.jpg  =  xe-y
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q19g7.jpg  = ye-y;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q19g8.jpg  =  xe-y(1 - y)
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q19g5.jpg  = ye-y;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q19g6.jpg  =  - xye-y
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q19g9.jpg  = ye-y;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q19g10.jpg  =  xe-y(y - 1)

2 points  

Question 45

1.  

Find fx, fy, and fz. f(x, y, z) = xz

		fx = z C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q22g5.jpg ; fy = -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q22g6.jpg ; fz = x C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q22g7.jpg
		fx = z C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q22g8.jpg ; fy =  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q22g9.jpg ; fz = x C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q22g10.jpg
		fx = z C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q22g2.jpg ; fy = -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q22g3.jpg ; fz = x C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q22g4.jpg
		fx = z C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q22g11.jpg ; fy =  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q22g12.jpg ; fz = x C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q22g13.jpg

2 points  

Question 46

1.  

Find the length and direction (when defined) of u × v. u = 6i, v = 6j

		36; -k
		36; k
		36; 36k
		6; 6k

2 points  

Question 47

1.  

Find the length and direction (when defined) of u × v. u = -4i + 3j - 5k, v = 8i - 6j + 10k

		0; no direction
		0; 4i- 3j + 5k
		5 C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q38g3.jpg ;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q38g4.jpg (4i - 3j + 5k)
		5 C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q38g1.jpg ;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q38g2.jpg (4i - 3j + 5k)

2 points  

Question 48

1.  

Evaluate the double integral over the given region.

 R = {(x, y): 9 ≤ x ≤ 10, 9 ≤ y ≤ 10}

		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q6g4.jpg 2
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q6g3.jpg 2
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q6g5.jpg
		ln  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q6g2.jpg

2 points  

Question 49

1.  

Find 

 and 

C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q18g2.jpg

. f(x, y) = 

C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q18g3.jpg

		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q18g12.jpg  =  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q18g13.jpg ;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q18g14.jpg  =  -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q18g15.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q18g4.jpg  =  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q18g5.jpg ;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q18g6.jpg  =  -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q18g7.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q18g16.jpg  =  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q18g17.jpg ;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q18g18.jpg  =   C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q18g19.jpg
		C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q18g8.jpg  = -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q18g9.jpg ;  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q18g10.jpg  =  -  C:\Users\test\Desktop\Take Test_ W8 Final – MA312 Calculus II (31-AUG-16 - 25..._files\f1q18g11.jpg

2 points  

Question 50

1.  

Find the general solution for the differential equation.

 = 18x2 - 14x

		y = 6x3 - 14x2 + C
		y = 6x3 - 7x2 + C
		y = 18x3 - 7x2 + C
		y = 18x3 - 14x2 + C

2 points