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Math 106a Quiz 5: Taylor Polynomials and Integrals, Exercises of Calculus

Aliah UniversityCalculus

The fifth quiz for math 106a, a college-level calculus course. The quiz covers topics on taylor polynomials and integrals. Students are required to find the fifth-order taylor polynomial of a given function, and use it to estimate the natural logarithm of a number. Additionally, they need to determine if a definite integral converges or diverges.

Typology: Exercises

2012/2013

Uploaded on 03/16/2013

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Math 106a Name
Quiz 5
10/29/10
Read directions carefully and show your work. Partial credit will be assigned based upon the correctness, com-
pleteness, and clarity of your answers.
1. Let f(x) = ln(1 −x).
(a) Find the 5th-order Taylor polynomial of f(x) centered at x= 0. Simplify your expression.
(b) Use the Taylor polynomial P5(x) to find an estimate for ln(0.5).
2. Does Zπ/2
0
sin x
√cos xdx converge or diverge?
1

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Math 106a Name Quiz 5 10/29/

Read directions carefully and show your work. Partial credit will be assigned based upon the correctness, com- pleteness, and clarity of your answers.

  1. Let f (x) = ln(1 − x).

(a) Find the 5th-order Taylor polynomial of f (x) centered at x = 0. Simplify your expression.

(b) Use the Taylor polynomial P 5 (x) to find an estimate for ln(0.5).

  1. Does

∫ (^) π/ 2

0

sin x √ cos x

dx converge or diverge?