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Values - Multivariable - Exam, Exams of Calculus

Bharat Ratna Dr. B. R. Ambedkar UniversityCalculus

Key points of this exam paper are: Values, Differentiable Function, Given Part, Problem, Completed, Compute, Evaluate, Explain, Initial Guess, Approximations

Typology: Exams

2012/2013

Uploaded on 03/21/2013

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Name:
Mathematics 105
Exam II
November 11, 2011
Problem Possible Actual
1 20
2 20
3 15
4 5
5 15
6 25
Total 100
You must show all work to receive credit.
No electronic devices other than calculators are permitted.
Give exact answers (such as ln5 or e2) unless requested otherwise.
pf3
pf4
pf5

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Name:

Mathematics 105 Exam II November 11, 2011

Problem Possible Actual 1 20 2 20 3 15 4 5 5 15 6 25 Total 100

You must show all work to receive credit. No electronic devices other than calculators are permitted. Give exact answers (such as ln 5 or e^2 ) unless requested otherwise.

  1. Assume r(x) and s(x) are differentiable function with the following values r(2) = e^2 , s(2) = 1, r(1) = π, r′(2) = 3e^2 , s′(2) = − 1 , s(π) = e, r′(1) =

2, and s′(4) = 3. Compute H′(2) for the following or explain why a given part of the problem may not be completed.

(a) H(x) = r(s(x))

(b) H(x) =

r(x) s(x)

(c) H(x) = r(x)^2 s(x)

(d) H(x) = s(r(x))

(e) H(x) = r(x)s(x)

  1. Use Newton’s Method with an initial guess of x 0 = 3 to find the next two approximations to a solution of x^4 − 8 x^2 − 1 = 0.
  2. Find three initial guesses in the above problem that would cause Newton’s Method to fail. Justify your answer.
  1. Write sec

arctan

x^2 − 1

as an algebraic expression.