$\"\"$

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The function is $\"\"$ .

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The function is centered at $\"\"$ .

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Definition of Taylor series:

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If a function $\"\"$ has derivatives of all orders at $\"\"$ then the series $\"\"$ is called Taylor series for $\"\"$ at $\"\"$ .

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First find the successive derivatives of $\"\"$ .

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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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$\"\"$ .

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The series is centered at $\"\"$ .

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Find the values of the function at $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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Find the Taylor polynonial $\"\"$ .

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Taylor polynomia is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Graph the polynomials $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Graph of the polynomials $\"\"$ and $\"\"$ .

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$\"\"$ .