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Flashcards in Final Exam Deck (30)
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1
Q

What is the slope of the tangent line of the function f (x) = −2x ^2 + 3x − 1 at x = −2?

A

11

2
Q

Consider the function y = x^ 2 − 3x + 2. At what value of x is the slope of the tangent line equal to 5?

A

4

3
Q

What is the derivative of the function

f (x) = −10x^5?

A

-50x^4

4
Q

Find the derivative of:

f(x)=(x+3)^3/2 / (x−2)^3/2

A

f′(x)=−15(x−2)1^/2(x+3)^1/2/2(x−2)^3

5
Q

Compute dy/dx for y=√x2+1+1/√x^2+1

A

x^3(1+x^2)^−3/2

6
Q

What is the derivative of the function f(x)=xsinx+1cosx?

A

sinxcosx+x+sinx/cos^2x

7
Q

What is the equation of the line tangent to the curve y + ex = 2e^xy at the point (0, 1)?

A

y = x + 1

8
Q

A point moves along the x-axis with its position, x, at time t given by x (t) = t ^3 − 3t ^2 + 2t − 1.

Which of the following is the acceleration when
t = 2?

A

6

9
Q

Determine d^2/dx^2 [e^x−3]

A

e^x−3

10
Q

A ladder 25 feet long is leaning against a house. The base of the ladder is pulled away from the wall at a rate of 2 ft / sec. How fast is the top moving down the wall when the base of the ladder is 15 feet from the wall?

A

−3/2 ft/sec

11
Q

A box manufacturer is to make a closed box of volume 288 in3, where the base is a rectangle whose length is three times its width. What is the length of the box that uses the least amount of material?

A

12 in

12
Q

What are the critical points of the function f (x) = x ^4 − 6x^ 2 + 8x ?

A

x = -2, 1

13
Q

For which of the following intervals is the graph of f(x)=24/x^2+12 concave down?

A

(−2,2)

14
Q

Which of the following equations could be an equation of a horizontal asymptote of y=2x^2−7x+4/x−5?

A

There is no horizontal asymptote

15
Q

Evaluate the indefinite integral∫⎛⎝3√t2+13√t5⎞⎠dt

A

3/5t^5/3−3/2t^−2/3+C

16
Q

Evaluate the indefinite integral ∫(3t2√t3+t2+1+2t√t3+t2+1)dt.

A

2/3(t^3+t^2+1)^3/2+C

17
Q

Evaluate ∫16/3 x^1/3cot(x^4/3)dx

A

4ln∣sin(x^4/3)∣+C

18
Q

What is the area beneath the curve f(x)=x2√3−x^3 from x = −2 to x = −1?

A

2⋅11^3/2−16/9

19
Q

Determine the height from which an object must be dropped so that it will have the same speed in ft / s when it lands as the height in feet from which it was dropped.

A

64 ft

20
Q

What is the area of the shaded region shown in the figure below bounded by the curves y = 2x^ 2 − 1, y = x^ 2 − x + 1, and y = x^ 2 + x + 1?

A

7/3

21
Q

Find dG/dx if

G(x)=ln(√5x+1/5x−1)

A

dG/dx=−5/25x^2−1

22
Q

What is the limit of the function in the graph at x = 4?

A

The limit does not exist

23
Q

Compute the derivative of the function f(x)=2x^2+2e^x.

A

f′(x)=4x+2e^x

24
Q

What is the inverse of f(x)=x/1+2x

A

f−1(x)=x/1−2x

25
Q

Evaluate ∫dx/|x|√4x^2−1.

A

arcsec (2x) + C

26
Q

What is the area between the curves x=y^2−9 and x=−y^2+9 ?

A

72

27
Q

What is the volume of the solid of revolution obtained by rotating the region bounded by y=x,x=1, and the x-axis around the x-axis?

A

π/3

28
Q

The half-life of iodine-126 (I 126 ) is 13 days. Of an original sample of 1,000.0 grams, how may grams of I 126 will remain after 98 days? Give the answer to the nearest tenth of a gram.

A

5.4 g

29
Q

A force of 2x + 5 pounds at a point x feet from the origin moves an object from
x = 2 to x = 5. What is the work done?

A

36 ft-lb

30
Q

Evaluate lim x→1 lnx/x^2−1

A

1/2

Decks in AP Calculus AB Class (190):