Step 1:

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The expression is $\"\"$ \ \

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Consider, the function $\"\"$ .

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Error cannot exceed $\"\"$ . \ \

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$\"\"$ . \ \

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$\"\"$ . \ \

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$\"\"$ . \ \

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Formula for error in Taylor series is : $\"\"$ , Where $\"\"$ any number between $\"\"$ and $\"\"$ .

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The $\"\"$ value never exceed 1. \ \

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The derivative of function $\"\"$ is less than or equal to 1, for all values of $\"\"$ .

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$\"\"$ , Where $\"\"$ any number between $\"\"$ and $\"\"$ . \ \

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

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$\"\"$

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

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$\"\"$

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$\"\"$ .

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$\"\"$ \ \

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$\"\"$ .

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Step 2: \ \

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Find $\"\"$ value by trial and error method. \ \

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Take $\"\"$ and substitute in $\"\"$ .

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$\"\"$

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$\"\"$ not possible. \ \

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Take $\"\"$ and substitute in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ , the statement is false. \ \

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Take $\"\"$ and substitute in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ , statement is false. \ \

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Take $\"\"$ and substitute in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ , the statement is true. \ \

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So, degree of the Maclaurin polynomial is $\"\"$ .

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Solution: \ \

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Degree of the Maclaurin polynomial is $\"\"$ . \ \