Series Representation - Calculus - Quiz, Exercises of Calculus

This is class quiz. Its from Calculus class. Some key points are: Series Representation, Power Series, Function, Convergence, Radius, Carefully, Find

Typology: Exercises

2012/2013

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MATH 106A - CALCULUS II
FALL 2005
QUIZ 10
NAME:
Show ALL your work CAREFULLY.
(a) Find a pwer series representation of the followingfunction f(x) and the radius
of convergence of the power series.
f(x) = sin(x)
(b) Use the pwoer series representation of 1
1tto give a power series representa-
tion of ln(1 + x2). [Hint: find a power series representation of 2x
1+x2first.]
Date: December 5, 2005.
1

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MATH 106A - CALCULUS II

FALL 2005

QUIZ 10

NAME:

Show ALL your work CAREFULLY.

(a) Find a pwer series representation of the following function f(x) and the radius

of convergence of the power series.

f(x) = sin(

x)

(b) Use the pwoer series representation of

1 1 −t to give a power series representa-

tion of ln(1 + x^2 ). [Hint: find a power series representation of

2 x 1+x^2

first.]

Date: December 5, 2005.

1