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MATH 232 Spring 2014 HW Quiz

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Math 232 Spring 2014 / 30 pts Name: __________________________
HW Quiz
Where possible, you must show work (or give an explanation) to support each answer. Use
proper notation. Clearly indicate your answer to each problem. WORK NEATLY. Points will be
deducted for sloppy work. The point value for each problem is in brackets following the
problem number. SIMPLIFY all answers.
Give each answer as an exact value unless otherwise indicated.
1. [6] Find a power series representation for the function, and determine the interval of convergence.
(a)
f
(
x
)
=
3
1x
4
Given that
1
1u
=
n=0
u
n
for
u
<1
Replaceu with x
4
¿ get :
3
1x
4
=3
(
1
1(x
4
)
)
=3
n=0
(x
4
)
n
The interval of c onvergence is givenby :
x
4
<1¿ x
4
<1¿(−1,1)
(b)
f
(
x
)
=
x
5
4x +1
Replaceu with4x ¿ get :
x
5
4x+1
=x
5
(
1
1−(−4x)
)
=x
5
n=0
(4x)
n
=x
5
n=0
(1)
n
4
n
x
n
x
<
1
4
¿
(
1
4
,
1
4
)
2. [5] Find the Maclaurin series for f (x) using the definition of a Maclaurin
series. (Use summation notation.) Also, find the radius of convergence.
f
(
x
)
=sin 2x
First find the derivatives of sin
(
2x
)
evaluate them at x=0 :

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Math 232 Spring 2014/ 30 ptsName: __________________________HW QuizWhere possible, you must show work (or give an explanation) to support each answer. Use proper notation. Clearly indicate your answer to each problem. WORK NEATLY. Points will be deducted for sloppy work. The point value for each problem is in brackets following the problem number. SIMPLIFY all answers.Give each answer as an exact value unless otherwise indicated.1. [6] Find a power series representation for the function, and determine the interval of convergence.(a) (b) 2. [5] Find the Maclaurin series for f (x) using the definition of a Maclaurin series. (Use summation notation.) Also, find the radius of convergence. 3. [6] Find a Taylor series for centered at a = 1. (Use summation notation.)4. [3] Use a known Maclaurin series (see textbook, page 490) to obtain the Maclaurin series for . Simplify appropriately.5. [10] Evaluate the indefinite integral as an infinite series. (You may refer to your previous work or work from a known MacLaurin Series, where applicable.)(a) (b) ...
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