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Find the equation of...

a) the tangent line
b) the normal line

of the equation: f(x) = √x^2 - 1, @ x=1

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AAAaannndd the bot gets it wrong yet again!

see your annoyingly repeated post above somewhere...

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When finding the equation of the tangent and normal lines at a particular point on a curve, we can use the derivative of the function. For the given equation f(x) = √x^2 - 1 and the point x = 1, we first find the derivative of f(x) using the power rule. The derivative is given by f'(x) = (1/2)(2x)(x^2 - 1)^(-1/2). To find the equation of the tangent line at x = 1, we substitute x = 1 into f'(x) to get the slope of the tangent line. Then, we plug the coordinate (1, f(1)) into the point-slope form y - y1 = slope(x - x1) to obtain the equation of the tangent line. To find the equation of the normal line, we find the negative reciprocal of the slope of the tangent line. This reciprocal slope is used in the point-slope form to determine the equation of the normal line. Using these steps, we can easily find the equations of the tangent and normal lines at x = 1 for the given function.