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Flashcards in Final Exam Deck (30):
1

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

11

2

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

4

3

What is the derivative of the function
f (x) = −10x^5?

-50x^4

4

Find the derivative of:
f(x)=(x+3)^3/2 / (x−2)^3/2

f′(x)=−15(x−2)1^/2(x+3)^1/2/2(x−2)^3

5

Compute dy/dx for y=√x2+1+1/√x^2+1

x^3(1+x^2)^−3/2

6

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

sinxcosx+x+sinx/cos^2x

7

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

y = x + 1

8

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?

6

9

Determine d^2/dx^2 [e^x−3]

e^x−3

10

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?

−3/2 ft/sec

11

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?

12 in

12

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

x = -2, 1

13

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

(−2,2)

14

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

There is no horizontal asymptote

15

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

3/5t^5/3−3/2t^−2/3+C

16

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

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

17

Evaluate ∫16/3 x^1/3cot(x^4/3)dx

4ln∣sin(x^4/3)∣+C

18

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

2⋅11^3/2−16/9

19

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.

64 ft

20

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?

7/3

21

Find dG/dx if
G(x)=ln(√5x+1/5x−1)

dG/dx=−5/25x^2−1

22

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

The limit does not exist

23

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

f′(x)=4x+2e^x

24

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

f−1(x)=x/1−2x

25

Evaluate ∫dx/|x|√4x^2−1.

arcsec (2x) + C

26

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

72

27

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?

π/3

28

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.

5.4 g

29

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?

36 ft-lb

30

Evaluate lim x→1 lnx/x^2−1

1/2

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