# What is the equation of the normal line of #f(x)=sqrt(x-1)/(x^2-3)# at #x = 2#?

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To find the equation of the normal line of f(x) at x = 2, we need to determine the slope of the tangent line at x = 2 and then find the negative reciprocal of that slope to obtain the slope of the normal line.

First, we find the derivative of f(x) using the quotient rule:

f'(x) = [(x^2 - 3)(1/2(x-1)) - (sqrt(x-1))(2x)] / (x^2 - 3)^2

Next, we substitute x = 2 into f'(x) to find the slope of the tangent line at x = 2:

f'(2) = [(2^2 - 3)(1/2(2-1)) - (sqrt(2-1))(2(2))] / (2^2 - 3)^2

Simplifying this expression gives us the slope of the tangent line at x = 2.

Finally, we take the negative reciprocal of this slope to find the slope of the normal line.

Once we have the slope of the normal line, we can use the point-slope form of a line to find the equation of the normal line passing through the point (2, f(2)).

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When evaluating a one-sided 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 one-sided 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 one-sided 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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