The function is and , ,
(a)
Find the Taylor polynomial with degree at the number .
Definition of Taylor series:
If a function has derivatives of all orders at then the series
is called Taylor series for at .
First find the successive derivatives of .
Apply derivative on each side with respect to .
Find the values of the above functions at .
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The series is centered at .
Taylor series centered at .
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(b)
The taylors inequality is where .
Here , and .
Substitute in
in
Hence, .
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The value of ,hence the value of should be .
The taylors accuracy inequality is .
(c)
The value is .
Here .
Substitute and .
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Graph :
Graph the function .
Observe the graph:
The functions for small value of in the interval .
(a) .
(b)
(c)
Graph of the function is
The functions for small value of in the interval .
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