$\"\"$

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The function is $\"\"$ .

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Find the transformation that relates $\"\"$ to $\"\"$ , use $\"\"$ -substitution.

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Substitute $\"\"$ for $\"\"$ in $\"\"$ , equate the two functions and solve for $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ . \ \

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Therefore, $\"\"$ .

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Replace $\"\"$ with $\"\"$ in $\"\"$ .

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$\"\"$ .

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The power series is $\"\"$ .

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The series is converges for $\"\"$ .

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$\"\"$

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$\"\"$ \ \

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There are no solutions for the condition $\"\"$ , hence it is not considered. \ \

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$\"\"$ \ \

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$\"\"$ \ \

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$\"\"$

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$\"\"$ .

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The series converges for $\"\"$ .

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$\"\"$

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Find the sixth partial sum of the series $\"\"$ .

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The sixth partial sum of the series is

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$\"\"$

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$\"\"$ .

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Graph : \ \

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Graph the function $\"\"$ and sixth partial sum $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ for $\"\"$ . \ \

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Graph of the function $\"\"$ and sixth partial sum $\"\"$ .

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$\"\"$