$\"\"$

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The functions are $\"\"$ and $\"\"$ .

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(a)

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Consider $\"\"$ .

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The maclaurian polynomial of degree $\"\"$ is $\"\"$ .

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Consider $\"\"$ .

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The maclaurian polynomial of degree $\"\"$ is $\"\"$ .

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The partial polynomial $\"\"$ .

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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 functions are $\"\"$ and $\"\"$ .

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(b)

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Consider $\"\"$ .

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The maclaurian polynomial of degree $\"\"$ is $\"\"$ .

\

Consider $\"\"$ .

\

The maclaurian polynomial of degree $\"\"$ is $\"\"$ .

\

The partial polynomial $\"\"$ .

\

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

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$\"\"$

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$

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The functions are $\"\"$ .

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(C)

\

Consider $\"\"$ .

\

The maclaurian polynomial of degree $\"\"$ is $\"\"$ .

\

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

\

$\"\"$

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$

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(a) $\"\"$ .

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(b) $\"\"$ .

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(c) $\"\"$ .