Calculus
flcoman89
calculus.pdf
Kyle Taitt CSU Webwork
MATH 160 WeBWorK assignment M160-801-FA-4.1 due 11/07/2016 at 11:59pm MST
1. (1 point) Find an antiderivative for each of the following functions:
If f 0(s) = s4 + 3s + p
s, then f (s) =
If f 0(s) = p
s
3 + 4 p
s, then f (s) =
If f 0(r) = r2/3 + r4/3, then f (r) =
If f 0(q) = q�4/3 + q3, then f (q) =
If f 0(x) = x�3/4 + x2, then f (x) =
Answer(s) submitted:
• • • • •
(incorrect)
2. (1 point) Find an antiderivative for each of the following functions:
If f 0(s) = sin(4s), then f (s) =
If f 0(r) = sec2(6r)�csc2(2r), then f (r) =
If f 0(r) = cos(�2r), then f (r) =
If f 0(q) = sin(q/4)+sin(4q), then f (q) =
If f 0(s) = csc2(6s), then f (s) =
Answer(s) submitted:
• • • • •
(incorrect)
3. (1 point) Evaluate the indefinite integral Z ✓
3 x
2 + 2
9x2
◆ dx
Answer(s) submitted:
•
(incorrect)
4. (1 point) Find the most general antiderivative or indefinite integral:
R 1 t
2 + t �3
dt = +C
R 3r2 + 3
p r + 2 dr = +C
R 1 x
3 + 1
3p x
2 dx = +C
R 8s2 + 6s1/2 + 3s4 ds = +C
R p q + 3q1/3 dq = +C
Answer(s) submitted:
• • • • •
(incorrect)
5. (1 point) Evaluate the following integrals:
R 6q3/4 + 3q�3/4 � 5q�7/3 + 5p1/3dq
+C
R 5s3 + 6s2 � 3s1/2 +
p pds +C
R 8x3 � x�2 � 16x3/5 + 4x�3/5dx +C
Answer(s) submitted:
• • •
(incorrect)
6. (1 point) Evaluate the following integrals:
R 2 tan t(sec t + cos t) dt +C
R cos s + 2 sec s tan s ds +C
R 3 cos r(1 + tan r) dr +C
Answer(s) submitted:
• • •
1
(incorrect)
7. (1 point) Evaluate the following integrals: Z
(3t � 2)(t + 1) t
2/3 dt +C
Z q
4 + 2q2 � 3 q
4 dq +C
Z (5 +
p r)
p r
dr +C
Answer(s) submitted:
• • •
(incorrect)
8. (1 point) Find a particular function which is an indefinite integral for:
Z (4x + sec(x)tan(x))dx
Answer(s) submitted:
•
(incorrect)
9. (1 point) Calculate the following antiderivatives:
(a) Z
13t � 6t 3 � 4 dt = +C.
(b) Z
1 u
1/4 + 7
p u du = +C.
(c) Z
1 5x6
dx = +C. Answer(s) submitted:
• • •
(incorrect)
10. (1 point) List corresponding features of the graphs of a function f , its first derivative f 0, and (an) antiderivative F . Describe a strategy whereby, given a plot showing the graphs of f , f 0, and F , you can determine which is which. Apply your strategy to identify the graphs A (blue), B (red) and C (green) as the graphs of a function f , its first derivative f 0, and (an) antiderivative F :
is the graph of the function f . is the graph of the function’s first derivative f 0. is the graph of an antiderivative of the function F .
Answer(s) submitted:
• • •
(incorrect)
11. (1 point) Consider the function f (x) = 2 x
2 � 6 x
7 . Let F(x)
be the antiderivative of f (x) with F(1) = 0. Then F(x) = Answer(s) submitted:
•
(incorrect)
12. (1 point) Consider the function f (x) = x5 + 8 p
x. Let F(x) be the antiderivative of f (x) with F(1) = �9. Then F(x) =
Answer(s) submitted:
•
(incorrect)
13. (1 point) Let f 000(t) = 3t + 8
p t.
(a) Find the most general formula for f 00(t). If an arbitrary constant must be used here, use an upper-case ”C”.
f
00(t) = 2
(b) Based on your answer to (a), find the most general for- mula for f 0(t). If another new arbitrary constant must be used here, use an upper-case ”D”.
f
0(t) = (c) Based on your answer to (b), find the most general for-
mula for f (t). If another new arbitrary constant must be used here, use an upper-case ”E”.
f (t) = Answer(s) submitted:
• • •
(incorrect)
14. (1 point) Find a function f such that f 0(x) = 5x3 and the line x + y = 0
is tangent to the graph of f . f (x) = Answer(s) submitted:
• (incorrect)
15. (1 point) Given that the graph of f passes through the point (1, 8) and
that the slope of its tangent line at (x, f (x)) is 2x + 1, find f (9). f (9) = Answer(s) submitted:
• (incorrect)
16. (1 point) The graph of a function f is shown below.
? 1. Which graph is an antiderivative of f ? Answer(s) submitted:
• (incorrect)
17. (1 point) Find the equation of the curve that passes through the point (5,5) if its slope is given by
dy
dx
= 2x � 2.
y =
Answer(s) submitted:
• (incorrect)
18. (1 point) Find the function g(x) satisfying the two condi- tions: 1. g0(x) = �1000 � x3 2. The maximum value of g(x) is 5. g(x) =
Answer(s) submitted:
• (incorrect)
19. (1 point) Find f if f 000(x) = sin(x), f (0) = �2, f 0(0) = �8, f 00(0) =
�1. f (x) = Answer(s) submitted:
• (incorrect)
20. (1 point) Find a particular function which is an indefinite integral for: Z
(3x + sec(x)tan(x))dx
Answer(s) submitted:
• (incorrect)
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