Calculus Quiz

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QUESTION 1

1. Find the limit if it exists. C:\Users\john.morris\Desktop\f1q17g1.jpg (x + 3)2(x - 3)3

25

-3125

1

-125

2 points   

QUESTION 2

1. Find the domain of the function. f(x) = x2 + 8

{x|x ≥ -8}

{x|x ≠ -8}

all real numbers

{x|x > -8}

2 points   

QUESTION 3

1. Find the absolute extrema if they exist as well as where they occur. f(x) = 3 - x - 25/x, x > 0

Absolute maximum of 13 at x = -5; absolute minimum of 3 at x = 0

Absolute minimum of -7 at x = 5; no absolute maximum

Absolute maximum of -23 at x = 1; no absolute minimum

Absolute maximum of -7 at x = 5; no absolute minimum

2 points   

QUESTION 4

1. Find the intervals on which the function is continuous. y = C:\Users\john.morris\Desktop\f1q25g1.jpg

discontinuous only when x = -3

discontinuous only when x = -24

discontinuous only when x = 15

continuous everywhere

2 points   

QUESTION 5

1. Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. log238 14 + log238 17

17

1

14

238

2 points   

QUESTION 6

1. Find the absolute extrema if they exist as well as where they occur. f(x) = -3x4 + 16x3 - 18x2 + 9

No absolute extrema

Absolute maximum of 36 at x = 3; no absolute minima

Absolute maximum of 17 at x = 2; no absolute minima

Absolute maximum of 4 at x = 1; no absolute minima

2 points   

QUESTION 7

1. Solve the equation. e2x = 7

{2 ln 7}

C:\Users\john.morris\Desktop\f1q37g1.jpg

C:\Users\john.morris\Desktop\f1q37g3.jpg

C:\Users\john.morris\Desktop\f1q37g2.jpg

2 points   

QUESTION 8

1. Find the limit. C:\Users\john.morris\Desktop\f1q13g1.jpg (3x5 - 2x4 + 4x3 + x2 + 5)

41

57

169

105

2 points   

QUESTION 9

1. Find the limit. C:\Users\john.morris\Desktop\f1q15g1.jpg C:\Users\john.morris\Desktop\f1q15g2.jpg

does not exist

0

- C:\Users\john.morris\Desktop\f1q15g3.jpg

1

2 points   

QUESTION 10

1. Determine if the given function can be extended to a continuous function at x=0.  If so, approximate the extended function's value at x=0 (rounded to four decimal places if necessary). If not, determine whether the function can be continuously extended from the left or from the right and provide the values of the extended functions at x=0. Otherwise write "no continuous extension." f(x) = (1 + 2x)1/x

f(0) = 7.3891

f(0) = 5.4366

No continuous extension

f(0) = 2.7183

2 points   

QUESTION 11

1. Find the integral. C:\Users\john.morris\Desktop\f1q4g1.jpg

C:\Users\john.morris\Desktop\f1q4g4.jpgx3/2 - C:\Users\john.morris\Desktop\f1q4g5.jpg + C

C:\Users\john.morris\Desktop\f1q4g4.jpgx3/2 - C:\Users\john.morris\Desktop\f1q4g9.jpg + C

2xC:\Users\john.morris\Desktop\f1q4g2.jpg - C:\Users\john.morris\Desktop\f1q4g9.jpg + C

2xC:\Users\john.morris\Desktop\f1q4g2.jpg - C:\Users\john.morris\Desktop\f1q4g5.jpg + C

2 points   

QUESTION 12

1. Find the intervals on which the function is continuous. y = C:\Users\john.morris\Desktop\f1q26g1.jpg

discontinuous only when x = 2

discontinuous only when x = 2 or x = 5

discontinuous only when x = -5 or x = 2

discontinuous only when x = -2 or x = 5

2 points   

QUESTION 13

1. Find the integral. C:\Users\john.morris\Desktop\f1q2g1.jpg

C:\Users\john.morris\Desktop\f1q2g6.jpgx3/2 + C:\Users\john.morris\Desktop\f1q2g7.jpgx4/3 + C

2C:\Users\john.morris\Desktop\f1q2g4.jpg + 2C:\Users\john.morris\Desktop\f1q2g5.jpg + C

C:\Users\john.morris\Desktop\f1q2g7.jpgx3/2 + C:\Users\john.morris\Desktop\f1q2g3.jpgx4/3 + C

2C:\Users\john.morris\Desktop\f1q2g4.jpg + 3C:\Users\john.morris\Desktop\f1q2g5.jpg + C

2 points   

QUESTION 14

1. Find the intervals on which the function is continuous. y = C:\Users\john.morris\Desktop\f1q24g1.jpg - 4x

continuous everywhere

discontinuous only when x = 3

discontinuous only when x = -7

discontinuous only when x = -3

2 points   

QUESTION 15

1. Find the integral. C:\Users\john.morris\Desktop\f1q5g1.jpg

- C:\Users\john.morris\Desktop\f1q5g4.jpg - C:\Users\john.morris\Desktop\f1q5g5.jpg + C

C:\Users\john.morris\Desktop\f1q5g4.jpg + C:\Users\john.morris\Desktop\f1q5g5.jpg + C

- C:\Users\john.morris\Desktop\f1q5g4.jpg + C:\Users\john.morris\Desktop\f1q5g5.jpg + C

C:\Users\john.morris\Desktop\f1q5g4.jpg - C:\Users\john.morris\Desktop\f1q5g5.jpg + C

2 points   

QUESTION 16

1. Find the domain of the function. h(x) = C:\Users\john.morris\Desktop\f1q48g1.jpg

{x|x ≠ 0}

{x|x ≠ 2}

{x|x ≠ -8, 0, 8}

all real numbers

2 points   

QUESTION 17

1. Solve the equation. e x + 6 = 8

{ln 14}

{e48}

{e8 + 6}

{ln 8 - 6}

2 points   

QUESTION 18

1. Find the domain of the function. C:\Users\john.morris\Desktop\f1q50g1.jpg

{x|x ≥ 6}

{x|x ≠ 6}

{x|x > 6}

all real numbers

2 points   

QUESTION 19

1. Find the domain of the function. f(x) = C:\Users\john.morris\Desktop\f1q49g1.jpg

{x|x ≠ 23}

{x|x ≠ C:\Users\john.morris\Desktop\f1q49g3.jpg}

{x|x ≤ C:\Users\john.morris\Desktop\f1q49g3.jpg}

{x|x ≤ 23}

2 points   

QUESTION 20

1. Determine if the given function can be extended to a continuous function at x=0  If so, approximate the extended function's value at x=0 (rounded to four decimal places if necessary). If not, determine whether the function can be continuously extended from the left or from the right and provide the values of the extended functions at x=0 Otherwise write "no continuous extension."

f(x) =  C:\Users\john.morris\Desktop\f1q30g4.jpg

f(0) = 2 only from the left

No continuous extension

f(0) = 2 

f(0) = 2 only from the right

2 points   

QUESTION 21

1. Find the domain of the function. g(x) = C:\Users\john.morris\Desktop\f1q47g1.jpg

all real numbers

{x|x > 49}

{x|x ≠ -7, 7}

{x|x ≠ 0}

2 points   

QUESTION 22

1. Solve the equation. 3 + 8 ln x = 10

{e 7/8}

C:\Users\john.morris\Desktop\f1q35g3.jpg

C:\Users\john.morris\Desktop\f1q35g1.jpg

C:\Users\john.morris\Desktop\f1q35g2.jpg

2 points   

QUESTION 23

1. Find the limit, if it exists. C:\Users\john.morris\Desktop\f1q21g1.jpg C:\Users\john.morris\Desktop\f1q21g2.jpg

C:\Users\john.morris\Desktop\f1q21g3.jpg

C:\Users\john.morris\Desktop\f1q21g4.jpg

17x

Does not exist

2 points   

QUESTION 24

1. Find the limit. C:\Users\john.morris\Desktop\f1q12g1.jpg (x3 + 5x2 - 7x + 1)

15

0

does not exist

29

2 points   

QUESTION 25

1. Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. log5 30 - log5 6

5

1

30

6

2 points   

QUESTION 26

1. Find the intervals on which the function is continuous. y = C:\Users\john.morris\Desktop\f1q27g1.jpg

discontinuous only when x = -16 or x = 16

discontinuous only when x = -4 or x = 4

discontinuous only when x = -4

discontinuous only when x = 16

2 points   

QUESTION 27

1. Determine if the given function can be extended to a continuous function at x=0  If so, approximate the extended function's value at x=0 (rounded to four decimal places if necessary). If not, determine whether the function can be continuously extended from the left or from the right and provide the values of the extended functions at x=0 Otherwise write "no continuous extension."

f(x) =C:\Users\john.morris\Desktop\f1q32g4.jpg 

No continuous extension

f(0) = 1

f(0) = 1 only from the left

f(0) = 1 only from the right

2 points   

QUESTION 28

1. Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.

ln e2 C:\Users\john.morris\Desktop\f1q40g1.jpg

8

2C:\Users\john.morris\Desktop\f1q40g1.jpg

64

e

2 points   

QUESTION 29

1. Find the limit if it exists. C:\Users\john.morris\Desktop\f1q18g1.jpg C:\Users\john.morris\Desktop\f1q18g2.jpg

62

-62

C:\Users\john.morris\Desktop\f1q18g3.jpg

-C:\Users\john.morris\Desktop\f1q18g3.jpg

2 points   

QUESTION 30

1. Solve the equation. log42 (x2 - x) = 1

{-6, -7}

{1, 42}

{-6, 7}

{6, 7}

2 points   

QUESTION 31

1. Find the limit if it exists. C:\Users\john.morris\Desktop\f1q16g1.jpgx3/4

192

64

256

3/4

2 points   

QUESTION 32

1. Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. log4 24 - log4 6

24

1

6

4

2 points   

QUESTION 33

1. Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.

ln e2 C:\Users\john.morris\Desktop\f1q41g1.jpg

64

2C:\Users\john.morris\Desktop\f1q41g1.jpg

8

e

2 points   

QUESTION 34

1. Find the domain of the function. f(x) = C:\Users\john.morris\Desktop\f1q46g1.jpg

{x|x ≠ -4}

{x|x > -4}

all real numbers

{x|x ≠ 0}

2 points   

QUESTION 35

1. Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. log6 6-9

6

-54

-9

1

2 points   

QUESTION 36

1. Find the limit, if it exists. C:\Users\john.morris\Desktop\f1q20g1.jpg C:\Users\john.morris\Desktop\f1q20g2.jpg

1/2

1

2

Does not exist

2 points   

QUESTION 37

1. Find the limit. C:\Users\john.morris\Desktop\f1q14g1.jpg C:\Users\john.morris\Desktop\f1q14g2.jpg

does not exist

121

±11

11

2 points   

QUESTION 38

1. Find the integral. C:\Users\john.morris\Desktop\f1q6g1.jpg

C:\Users\john.morris\Desktop\f1q6g2.jpgx5 + ln C:\Users\john.morris\Desktop\f1q6g3.jpg + C

C:\Users\john.morris\Desktop\f1q6g2.jpgx5 - ln C:\Users\john.morris\Desktop\f1q6g3.jpg + C

C:\Users\john.morris\Desktop\f1q6g8.jpgx4 - ln C:\Users\john.morris\Desktop\f1q6g3.jpg + C

C:\Users\john.morris\Desktop\f1q6g8.jpgx4 + ln C:\Users\john.morris\Desktop\f1q6g3.jpg + C

2 points   

QUESTION 39

1. Find the integral. C:\Users\john.morris\Desktop\f1q1g1.jpg dx

C:\Users\john.morris\Desktop\f1q1g8.jpgx7/3 - C:\Users\john.morris\Desktop\f1q1g9.jpgx7/2 + C

C:\Users\john.morris\Desktop\f1q1g4.jpgx7/3 - C:\Users\john.morris\Desktop\f1q1g5.jpgx7/2 + C

C:\Users\john.morris\Desktop\f1q1g4.jpgx7/3 - C:\Users\john.morris\Desktop\f1q1g8.jpgx7/2 + C

C:\Users\john.morris\Desktop\f1q1g8.jpgx7/3 - C:\Users\john.morris\Desktop\f1q1g3.jpgx7/2 + C

2 points   

QUESTION 40

1. Find the integral. C:\Users\john.morris\Desktop\f1q1g1.jpgdx

7 ln C:\Users\john.morris\Desktop\f1q8g4.jpg - C:\Users\john.morris\Desktop\f1q8g5.jpge-0.7x + C

- C:\Users\john.morris\Desktop\f1q8g2.jpg + C:\Users\john.morris\Desktop\f1q8g3.jpge-0.7x + C

C:\Users\john.morris\Desktop\f1q8g8.jpg - C:\Users\john.morris\Desktop\f1q8g3.jpge-0.7x + C

7 ln C:\Users\john.morris\Desktop\f1q8g4.jpg + C:\Users\john.morris\Desktop\f1q8g5.jpge-0.7x + C

2 points   

QUESTION 41

1. Solve the equation. ln C:\Users\john.morris\Desktop\f1q36g1.jpg = 2

C:\Users\john.morris\Desktop\f1q36g2.jpg

{e4 - 2}

{e2 - 2}

{e4 + 2}

2 points   

QUESTION 42

1. Find the intervals on which the function is continuous. y = C:\Users\john.morris\Desktop\f1q28g1.jpg - C:\Users\john.morris\Desktop\f1q28g2.jpg

discontinuous only when x = -7 or x = -4

discontinuous only when x = -11

continuous everywhere

discontinuous only when x = -4

2 points   

QUESTION 43

1. Find the integral. C:\Users\john.morris\Desktop\f1q3g1.jpg

- C:\Users\john.morris\Desktop\f1q3g4.jpg - C:\Users\john.morris\Desktop\f1q3g5.jpg + C

C:\Users\john.morris\Desktop\f1q3g4.jpg - C:\Users\john.morris\Desktop\f1q3g5.jpg + C

- C:\Users\john.morris\Desktop\f1q3g4.jpg -  8C:\Users\john.morris\Desktop\f1q3g3.jpg + C

C:\Users\john.morris\Desktop\f1q3g4.jpg - 8C:\Users\john.morris\Desktop\f1q3g3.jpg - C

2 points   

QUESTION 44

1. Find the limit if it exists. C:\Users\john.morris\Desktop\f1q19g1.jpg (x - 24)1/3

-3

1

3

9

2 points   

QUESTION 45

1. Solve the equation. 9 ln 5x = 36

C:\Users\john.morris\Desktop\f1q34g1.jpg

{e4}

C:\Users\john.morris\Desktop\f1q34g3.jpg

C:\Users\john.morris\Desktop\f1q34g2.jpg

2 points   

QUESTION 46

1. Find the limit, if it exists. C:\Users\john.morris\Desktop\f1q23g1.jpg  C:\Users\john.morris\Desktop\f1q23g2.jpg

Does not exist

0

1/3

3

2 points   

QUESTION 47

1. Find the limit, if it exists. C:\Users\john.morris\Desktop\f1q22g1.jpg  C:\Users\john.morris\Desktop\f1q22g2.jpg

1/2

Does not exist

1/4

0

2 points   

QUESTION 48

1. Find the absolute extrema if they exist as well as where they occur. f(x) = C:\Users\john.morris\Desktop\f1q10g1.jpg

Absolute minimum of - C:\Users\john.morris\Desktop\f1q10g2.jpg at x = -4; absolute maximum of C:\Users\john.morris\Desktop\f1q10g3.jpg  at x = 5

Absolute minimum of - 1 at x = -3; absolute maximum of C:\Users\john.morris\Desktop\f1q10g3.jpg at x = 5

No absolute extrema

Absolute minimum of - 1 at x = -3; no absolute maxima

2 points   

QUESTION 49

1. Find the integral. C:\Users\john.morris\Desktop\f1q7g1.jpg

C:\Users\john.morris\Desktop\f1q7g9.jpg C:\Users\john.morris\Desktop\f1q7g10.jpg ln C:\Users\john.morris\Desktop\f1q7g11.jpg - 4x-1/2 + C

C:\Users\john.morris\Desktop\f1q7g9.jpg ln C:\Users\john.morris\Desktop\f1q7g11.jpg - 4x-1/2 + C

C:\Users\john.morris\Desktop\f1q7g9.jpg C:\Users\john.morris\Desktop\f1q7g10.jpg ln C:\Users\john.morris\Desktop\f1q7g11.jpg + 4x-1/2 + C

C:\Users\john.morris\Desktop\f1q7g9.jpg ln C:\Users\john.morris\Desktop\f1q7g11.jpg + 4x-1/2 + C

2 points   

QUESTION 50

1. Determine if the given function can be extended to a continuous function at x=0  If so, approximate the extended function's value at x=0 (rounded to four decimal places if necessary). If not, determine whether the function can be continuously extended from the left or from the right and provide the values of the extended functions at x=0 Otherwise write "no continuous extension."

f(x) = C:\Users\john.morris\Desktop\f1q29g4.jpg

f(0) = 0 only from the right

f(0) = 0

f(0) = 0 only from the left

No continuous extension