What is the equation of the line normal to # f(x)=x/(x2) # at # x=1#?
Equation of normal is
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The equation of the line normal to f(x)=x/(x2) at x=1 is y = 3x + 4.
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To find the equation of the line normal to ( f(x) = \frac{x}{x2} ) at ( x = 1 ), we first need to find the derivative of the function ( f(x) ), and then find the slope of the tangent line at ( x = 1 ). Since the normal line is perpendicular to the tangent line, its slope will be the negative reciprocal of the slope of the tangent line. Finally, we use the pointslope form to write the equation of the line.

Find the derivative of ( f(x) ): [ f'(x) = \frac{d}{dx}\left(\frac{x}{x2}\right) ]

Evaluate the derivative at ( x = 1 ) to find the slope of the tangent line: [ f'(1) = \frac{d}{dx}\left(\frac{x}{x2}\right) \bigg_{x=1} ]

Once we have the slope of the tangent line, we find the slope of the normal line, which is the negative reciprocal of the slope of the tangent line.

We then use the pointslope form of the equation of a line to find the equation of the normal line, using the given point ( (1, f(1)) ).
The equation of the line normal to ( f(x) = \frac{x}{x2} ) at ( x = 1 ) can be found using these steps.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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