$\"\"$

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

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(a) Without eliminating the parameter. \ \

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Consider $\"\"$ .

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Substitute the point $\"\"$ in $\"\"$ .

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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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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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Chain rule of derivatives : $\"\"$

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Substitute $\"\"$ and $\"\"$ in above expression.

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$\"\"$

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Substitute $\"\"$ .

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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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$\"\"$

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(b) By first eliminating the parameter.

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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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Logarithmic function definition: $\"\"$ .

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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 $\"\"$