# What is the equation of the line normal to # f(x)=1/(e^x+4)# at # x=6#?

We know the equation of a line is

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To find the equation of the line normal to f(x) = 1/(e^x+4) at x = 6, we need to determine the slope of the tangent line at x = 6 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, we can take the derivative of f(x) with respect to x.

The derivative of f(x) = 1/(e^x+4) is given by:

f'(x) = -e^x/(e^x+4)^2

Evaluating f'(x) at x = 6, we have:

f'(6) = -e^6/(e^6+4)^2

This gives us the slope of the tangent line at x = 6.

To find the slope of the normal line, we take the negative reciprocal of f'(6):

slope of normal line = -1/f'(6)

Finally, we can use the point-slope form of a line to find the equation of the line normal to f(x) at x = 6. We have the point (6, f(6)) and the slope of the normal line. Plugging these values into the point-slope form, we get:

y - f(6) = slope of normal line * (x - 6)

Simplifying this equation will give us the equation of the line normal to f(x) at x = 6.

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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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