$\"\"$

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The vector function is $\"\"$ .

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Find the limit of the function $\"\"$ .

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The component function $\"\"$ can be written as $\"\"$ .

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Then $\"\"$ can be written as $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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The function is in indeterminate form $\"\"$ , hence apply L $\"\"$ Hospital rule.

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L $\"\"$ Hospital rule: if the limit of the function $\"\"$ is in indeteminate form $\"\"$ or $\"\"$ , then $\"\"$ .

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$\"\"$ .

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Apply L $\"\"$ Hospital rule.

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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

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$\"\"$

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