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

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To find the equation of the normal line at x = 3 for the function f(x) = sqrt(e^(2x) - x^2)/(x - 1)^2, we need to determine the slope of the tangent line at x = 3 and then find the negative reciprocal of that slope to obtain the slope of the normal line.

To find the slope of the tangent line at x = 3, we can take the derivative of f(x) with respect to x and evaluate it at x = 3.

After finding the derivative, we substitute x = 3 into the derivative to obtain the slope of the tangent line.

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.

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