sampleExam-calculus-II.pdf

# sampleExam-calculus-II.pdf - — Problem 1[2 x 8 Points...

• Test Prep
• she.ali01
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Problem 1 [2 x 8 Points]: Consider the function f ( x ) = x 2 in the interval [0 , 1]. a) Derive the Riemann sum of f ( x ) on the given interval for a regular partition. b) Using the result from a) compute R 1 0 f ( x ) dx . Problem 2 [3 x 9 Points]: Compute the following indefinite integrals using substitution or integration by parts: a) Z 2 x p 1 + x 2 dx , b) Z dx p x (1 + p x ) 2 , c) Z x cos(3 x ) dx . Problem 3 [3 x 9 Points]: Consider the function g ( x ) = ln( x ). a) Compute the Taylor polynomial of order 3 for g ( x ) at x 0 = 2. b) Write down the Lagrange remainder for the Taylor polynomial that you derived in a). c) Compute the Taylor series of g ( x ) at x 0 = 2. Problem 4 [8 Points]:
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