$\"\"$

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(a)

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The parametric equations are $\"\"$ and $\"\"$ and the point is $\"\"$ .

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

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$\"\"$

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$\"\"$ , which also satisfies the equation $\"\"$ .

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$\"\"$

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The slope of the tangent line is $\"\"$ at $\"\"$ .

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Consider $\"\"$ .

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

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$\"\"$

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$\"\"$ .

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Consider $\"\"$ .

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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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Chain rule of derivatives: $\"\"$

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in above equation.

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$\"\"$

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The slope is $\"\"$ .

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The point-slope form of a line equation is $\"\"$ .

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Substitute $\"\"$ and the point $\"\"$ in above equation.

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$\"\"$

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The tangent line equation is $\"\"$ . $\"\"$

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(b)

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The functions are $\"\"$ and $\"\"$ and the point is $\"\"$ .

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The slope of the tangent line is the derivative of the function at $\"\"$ .

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Consider $\"\"$ .

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Rewrite the expression.

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$\"\"$

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

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$\"\"$

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

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$\"\"$

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Substitute $\"\"$ in above equation.

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$\"\"$

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The slope is $\"\"$ .

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$\"\"$

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The point-slope form of a line equation is $\"\"$ .

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Substitute $\"\"$ and the point $\"\"$ in above equation.

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$\"\"$

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The tangent line equation is $\"\"$ .

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$\"\"$

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The tangent line equation is $\"\"$ .