What is the equation of the line that is normal to #f(x)= ln(x^2+1)-2x #at # x= 1 #?

Answer 1

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Answer 2

To find the equation of the line that is normal to the function f(x) = ln(x^2+1) - 2x at x = 1, we need to determine the slope of the tangent line at x = 1 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 = 1, we can take the derivative of the function f(x) with respect to x and evaluate it at x = 1.

The derivative of f(x) = ln(x^2+1) - 2x is given by f'(x) = (2x/(x^2+1)) - 2.

Evaluating f'(x) at x = 1, we get f'(1) = (2(1)/(1^2+1)) - 2 = 0.

Since the slope of the tangent line at x = 1 is 0, the slope of the normal line will be the negative reciprocal of 0, which is undefined.

Therefore, the equation of the line that is normal to f(x) = ln(x^2+1) - 2x at x = 1 is undefined.

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Answer from HIX Tutor

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.

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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