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MA 125-5B, Spring 2004 Test #3: Calculus Problems, Exams of Calculus

Birla Institute of Technology and ScienceCalculus

The spring 2004 test #3 for ma 125-5b calculus class. The test includes 8 problems covering topics such as finding derivatives, evaluating limits, using newton's method, and graphing functions. Students are required to solve problems without using books, notes, or calculators.

Typology: Exams

2012/2013

Uploaded on 03/15/2013

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MA 125-5B, Spring 2004
TEST # 3
March 31, 2004 (70 minutes)
Name: SSN:
Max. Points: 100 + 5 Bonus Points: Test Grade:
Turn in all the work which you did to solve the problems, not just the final answer. In
particular, include intermediate steps in calculations, wherever they are needed.
You may write on the back of a page if you need extra space.
No book, no notes, and no calculator are to be used!
1. Find f0(x) for the following functions (3 ×5P):
(a) f(x) = xe3x
(b) f(x) = ln(x+√x)
pf3
pf4
pf5

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MA 125-5B, Spring 2004

TEST # 3

March 31, 2004 (70 minutes)

Name: SSN:

Max. Points: 100 + 5 Bonus Points: Test Grade:

Turn in all the work which you did to solve the problems, not just the final answer. In particular, include intermediate steps in calculations, wherever they are needed. You may write on the back of a page if you need extra space.

No book, no notes, and no calculator are to be used!

  1. Find f ′(x) for the following functions (3 × 5P): (a) f (x) = xe^3 x

(b) f (x) = ln(x +

x)

(c) f (x) =

( (^) sin x

cos x − 1

) 2

  1. Evaluate the following limits (3 × 5P):

(a) lim x→ 0

ex^ − 1 − x x^2

(b) lim x→∞ e−x^ ln x

(c) lim x→ 1

x^2 x + 1

  1. Find the absolute minimum and maximum values of f (x) = x− 2

x on the interval 0 ≤ x ≤ 9. (12P)

  1. (a) State the Mean Value Theorem. (3P)

(b)∗^ Check if the following is possible: A differentiable function f (x) on [0, 1] has the property that f (0) = 1, f (1) = 3 and f ′(x) ≤ 1 for all x in [0, 1]. If this is possible, find such a function. If it is not possible, explain why such a function does not exist. (5P∗)

  1. Let f (x) = x^3 − 3 x^2. (total: 20P)

(a) Find the intervals in which f is increasing/decreasing. (4P) (b) Find all local extreme values of f. (3P) (c) Determine the intervals where f is concave up, concave down. (4P) (d) Find the points of inflection of f. (3P) (e) Sketch the graph of f. (6P)