(a)
To find:First four nonzero terms in the Taylor series generated by f ( x ) at
(a)
Answer to Problem 27E
First four nonzero terms in the Taylor series are
Explanation of Solution
Given information:
At
For nonzero terms:
We have
First derivative:
Second derivative:
Third derivative:
Thus,
Therefore,
First four nonzero terms in the Taylor series are
(b)
To find:First four nonzero terms in the Taylor series for g ( x ) at
(b)
Answer to Problem 27E
For
The first four non − zero terms in Taylor series expansion of are
Explanation of Solution
Given information:
At
From Part (a) result,
We have
First four nonzero terms in the Taylor series are
Now,
Replace x in Taylor series expansion of f(x) with
Thus,
Therefore,
The first four non − zero terms in Taylor series expansion of
(c)
To find:First four nonzero terms in the Taylor series at
(c)
Answer to Problem 27E
The first four non − zero terms in Taylor series expansion of h ( x ) are:
Explanation of Solution
Given information:
And
We can get the Taylor series expansion of h ( x ) by integrating the terms of the Taylor series expansion of
The first four non − zero terms in Taylor series expansion of
Now,
Integrate above first four non − zero terms to get Taylor series expansion of h ( x ):
Therefore,
The first four non − zero terms in Taylor series expansion of h ( x ) are:
Chapter 10 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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