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Calc 1 4.7

 

<== Calculus 1
Number Question Answer
See the work
1. Find the antiderivatives for

dP/dx = 28 - 5 x.

P = + C.
The work

Point Cost: 1
2. Find the antiderivatives for

rac{dy}{du} = 4 u^{5} - 4 u^{2} - 4.

y = + C.
rac{dy}{du} = 4 u^{5} - 4 u^{2} - 4.
The work

Point Cost: 1
3. Find the antiderivatives for

rac{dy}{dx} = 7 e^x + 7.

y = + C.
rac{dy}{dx} = 7 e^x + 7x.
The work

Point Cost: 1
4. Consider the function f(x) = 20 x^3 - 12 x^2 + 16 x - 1. Enter an antiderivative of f(x)
f(x) = 5 x^4 - 4 x^3 + 8 x^2 - 1x
The work

Point Cost: 1
5. Find the most general antiderivative for the function y(t) = \displaystyle{ 8 x^{1/2} }.
Antiderivative of y(t) = + C.
y(t) =
The work

Point Cost: 1
6. Find the most general antiderivative for the function \displaystyle{ rac{1}{3 \sqrt{u}}}.
Antiderivative = + C.
The work

Point Cost: 1
7. Find the most general antiderivative for the function \displaystyle{ \left(7 x^4 - rac{5}{x^{3}} - 3
ight)}.
Antiderivative = + C.
\displaystyle{ \left(7 x^4 - rac{5}{x^{3}} - 3
ight)}
The work

Point Cost: 1
8. Let \displaystyle f(x) = rac{6}{x} - 10 e^x.
Enter an antiderivative of f(x)
\displaystyle f(x) = rac{6}{x} - 10 e^x
The work

Point Cost: 0
9. Find the antiderivatives for

rac{dx}{dt} = 7 t^{-1} + 5.

x = + C.
rac{dx}{dt} = 7 t^{-1} + 5.
The work

Point Cost: 1
10. Let \displaystyle f(x) = rac{-17}{\sqrt{1-x^2}}.
Enter an antiderivative of f(x)
+ C
\displaystyle f(x) = rac{-17}{\sqrt{1-x^2}}
The work

Point Cost: 1
11. Let \displaystyle f(x) = rac{6}{x^2+1}.
Enter an antiderivative of f(x)
\displaystyle f(x) = rac{6}{x^2+1}
The work

Point Cost: 1
12. Find the most general antiderivative for the function \displaystyle{ 6 \sqrt{x} + rac{6}{\sqrt{x}}}.
Antiderivative = + C.
\displaystyle{ 6 \sqrt{x} + rac{6}{\sqrt{x}}}
The work

Point Cost: 1
13. Find the most general antiderivative for the function \displaystyle{ rac{6}{\sqrt[3]{x}} - 3 \sqrt[3]{x^2}}.
Antiderivative = + C.
\displaystyle{ rac{6}{\sqrt[3]{x}} - 3 \sqrt[3]{x^2}}
The work

Point Cost: 1
14. Find an antiderivative for \displaystyle{ rac{6 x^4 - 5 x}{x^3}}.

Antiderivative =
\displaystyle{ rac{6 x^4 - 5 x}{x^3}}
The work

Point Cost: 1
15. Find an antiderivative for the function \displaystyle{ rac{2 - 3 x^4}{x^2}}.

Antiderivative =
\displaystyle{ rac{2 - 3 x^4}{x^2}}.
The work

Point Cost: 1
16. Find an antiderivative for the function \displaystyle{ rac{2 - 5 x e^x}{x}}.

Antiderivative =

\displaystyle{ rac{2 - 5 x e^x}{x}}
The work

Point Cost: 1
17. Find the particular antiderivative that satisfies the following conditions:

R'(x) = 7  - 0.8 x; \quad R(0) = 6.


R(x) =
R'(x) = 7  - 0.8 x; \quad R(0) = 6.
The work

Point Cost: 2
18. Consider the function \displaystyle  f(x) = rac { 7 }{ x^ {3} } - rac { 3 }{ x^ { 7 }}.
Let F(x) be the antiderivative of f(x) with F(1) = 0.
Then F(x) =
\displaystyle  f(x) = rac { 7 }{ x^ {3} } - rac { 3 }{ x^ { 7 }}
The work

Point Cost: 2
19. Consider the function f(t) =  8 \sec ^2(t) - 9 t^ { 2 }. Let F(t) be the antiderivative of f(t) with F(0) = 0.
Then F(t) equals
f(t) =  8 \sec ^2(t) - 9 t^ { 2 }
The work

Point Cost: 2
20. Given f'(x) = 7 \cos x - 15 \sin x and f(0) = 5,

find f(x) =

f'(x) = 7 \cos x - 15 \sin x
The work

Point Cost: 2
21. Find the particular antiderivative that satisfies the following conditions:

p'(x) = -rac{50}{x^2}; \quad p(3) = 7.


p(x) =
p'(x) = -rac{50}{x^2}; \quad p(3) = 7.
The work

Point Cost: 2
22. Find the particular antiderivative that satisfies the following conditions:

p'(x) = rac{40}{x^3}; \quad p(2) = 7.


p(x) =
p'(x) = rac{40}{x^3}; \quad p(2) = 7.
The work

Point Cost: 2
23. Find the particular antiderivative that satisfies the following conditions:

rac{dM}{dt} = rac{6 t^2 - 6}{t^2}; \quad M(4) = 3.


M =
M = rac{dM}{dt} = rac{6 t^2 - 6}{t^2}; \quad M(4) = 3.
The work

Point Cost: 2
24. Find the particular antiderivative that satisfies the following conditions:

rac{dy}{dx} = rac{7 x + 6}{\sqrt[3]{x}}; \quad y(1) = 7.


y =
rac{dy}{dx} = rac{7 x + 6}{\sqrt[3]{x}}; \quad y(1) = 7.
The work

Point Cost: 2
25. Find the particular antiderivative that satisfies the following conditions:

rac{dx}{dt} = rac{5 \sqrt{t^3} - 5 t}{\sqrt{t^3}}; \quad x(9) = 2.


x =
rac{dx}{dt} = rac{5 \sqrt{t^3} - 5 t}{\sqrt{t^3}}; \quad x(9) = 2.
The work

Point Cost: 2
26. Consider the function f(x) whose second derivative is f''(x) = 5 x + 6 \sin (x). If f(0) = 2 and f'(0) = 4, what is f(x)?
f''(x) = 5 x + 6 \sin (x)
The work

Point Cost: 3
27. Given f'''(x) = e^x with f''(0)=4, f'(0)=6,
then f(x) = + C.
f'''(x) = e^x
The work

Point Cost: 3
28. Given that the graph of f(x) passes through the point ( 2, 9 ) and that the slope of its tangent line at (x , f(x)) is 3 x + 5, what is f(5)?   f  (5) = 55.5
The work

Point Cost: 3
29. A particle is moving with acceleration a(t) = 30 t + 2. its position at time t =0 is s(0) = 15 and its velocity at time t =0 is v(0) = 5. What is its position at time t = 11?   s (11) = 6846
The work

Point Cost: 3
30. A car traveling at 43 ft/sec decelerates at a constant 4 feet per second squared. How many feet does the car travel before coming to a complete stop?

231.125 ft
The work

Point Cost: 3
31. A ball is shot straight up into the air with initial velocity of 48 ft/sec. Assuming that the air resistance can be ignored, how high does it go?

*Acceleration due to gravity is 32 ft/sec^2

36 ft
The work

Point Cost: 3
32. A stone is thrown straight up from the edge of a roof, 675 feet above the ground, at a speed of 20 feet per second.
A. The acceleration due to gravity is -32 feet per second squared,
how high is the stone 4 seconds later?
B. At what time does the stone hit the ground?
C. What is the velocity of the stone when it hits the ground?
A) 499 ft

B) 7.15 s

C) -208.81 ft/sec
The work

Point Cost: 3
33. A stone is dropped from the edge of a roof, and hits the ground with a velocity of -200 feet per second. How high (in feet) is the roof? 625 ft
The work

Point Cost: 3