Math 140 -- Practice problems for Midterm II

from Professor Dennis DeTurck's webpage

Do these 13 problems and hand in your work during recitation the week of November 16. Your solutions to these problems will be used to improve your grade on Midterm II. Please show all your work, and also attach a cover sheet on which you indicate your letter choices. You may not work with other students on these problems. We ask you to sign the statement "I have observed the honor code" on your cover sheet to indicate that you have not collaborated with other students in working on these problems during the time from when they were assigned (November 12) until the solutions are due (November 17 or 19, depending on your recitation section). However, you should feel free to discuss the relevant material and problem-solving techniques with the instructor or the TAs. You may also consult any of the university's calculus help facilities. Good luck.

1. Find the area under the graph of between x=0 and .

A. 0

B.

C. 3/2

D.

E.

2. What is the output of the Maple statement:

> evalf(Int(x^3*sqrt(x^4+1),x=0..3^(1/4)));

A. 0.0000000000

B. 1.3333333333

C. 1.1414213562

D. 1.1666666667

E. 4.0000000000

3. You have been asked to design a 1-liter oil can shaped like a right circular cylinder (that includes a top and a bottom). You wish to use the least amount of material possible (i.e., to minimize the surface area of the drum). What should the relationship between the radius r of the can and the height h of the can be?

A. h = 2r

B. h = r

C.

D. h = r/2

E.

4. The graph of is concave down for

A. -2 < x < 2

B. < x <

C. < x <

D. < x <

E. < x <

5. =

A. 3

B. 1/9

C. -4/3

D. 4/9

E. 27

6. =

A.

B.

C.

D.

E.

7. Find the minimum distance between the parabola and the origin.

A. -1

B. 0

C.

D. 3/4

E. 1

8. Tracey and Alice decided they wanted to raise llamas in a rectangular field, along a straight river, with an area of 100 square kilometers. What is the least amount of fencing needed, assuming that no fencing is needed along the river (since the llamas can't swim)?

A. 30 km

B. 40 km

C. 100 km

D. km

E. km

9. Let . What is F'(0) ?

A.

B.

C.

D. 0

E.

10. For which of the following functions f(x) must there be a value of x in the closed interval [-1,1] such that f '(x) = 0 ?

A.

B.

C.

D.

E.

11. The graph of . has a horizontal asymptote:

A. x = 3

B. x = 1/3

C. y = 3

D. y = 1/3

E. The graph has no horizontal asymptote

12. The graph of is increasing on

A. the interval (-1, 1) only

B. the interval (1, ) only

C. the interval ( ,-1) and the interval (1, ) only

D. the interval (-1,0) and the interval ( ) only

E. the interval ( ) and the interval (0,1) only

13. Which of the following best describes the graph of ?

A. strictly increasing on [-1,1], concave down for x negative, concave up for x positive, with inflection point at origin

B. nonnegative on all of [-1,1], local minimum at origin and local maxima at around x = 0.8 and -0.8

C. decreasing to a local min somewhere around x = -0.7, then increasing, with inflection point at origin, reaching a local max around x = 0.7, then decreasing again

D. concave down on [-1,1], increasing until around x = 0.7, and then decreasing

E. negative for x negative and positive for x positive, with extreme points at around x = -0.8 and 0.8, inflection points at around x = -0.4 and 0.4, and horizontal tangent line at origin (which is a third inflection point)