$\"\"$

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The function is $\"\"$ .

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$\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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The power series form of $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$ .

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Apply integral on each side.

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$\"\"$

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$\"\"$ .

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Find the value of $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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When $\"\"$ , the value of $\"\"$ .

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Hence the value of $\"\"$ .

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The function is $\"\"$ .

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Expand the expression $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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Graph :

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Graph the function $\"\"$ .

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Graph the partial sums are $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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Observe the graph :

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As the value of $\"\"$ increases the approximation gets closer to $\"\"$ over a wider interval.

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$\"\"$

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The power series is $\"\"$

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Graph :

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Graph of the function $\"\"$ .

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Graph of the partial sums are $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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As the value of $\"\"$ increases the approximation gets closer to $\"\"$ over a wider interval.