$\"\"$

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The function is $\"\"$ .

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Maclaurin series is $\"\"$ .

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Find consecutive derivatives of the function to know the pattern of the n th derivative of the function.

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$\"\"$ .

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Differentiate with respect to $\"\"$ on each side.

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$\"\"$

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$\"\"$

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$\"\"$

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Similarly, we can write $\"\"$ .

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Find the values of the above functions at 0.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute above values in the Maclaurin series formula.

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$\"\"$

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Maclaurin series of the function $\"\"$ is $\"\"$ .

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$\"\"$

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Find the radius of convergence using ratio test.

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The series is $\"\"$ .

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Consider $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Therefore irrespective of $\"\"$ values series is convergent for all $\"\"$ .

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Interval of convergence is $\"\"$ .

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Hence the radius of convergence is $\"\"$ .

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$\"\"$

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Maclaurin series of the function $\"\"$ is $\"\"$ .

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Radius of convergence is $\"\"$ .

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