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

Equation of normal line would be

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To find the equation of the line that is normal to the function f(x) = e^(2x) sqrt(2x+2) 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, 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) = e^(2x) sqrt(2x+2) can be found using the product rule and chain rule.

After taking the derivative and evaluating it at x=1, we obtain the slope of the tangent line.

Next, we find the negative reciprocal of this slope to obtain the slope of the normal line.

Finally, using the point-slope form of a line, we can write the equation of the line that is normal to f(x) at x=1 using the slope of the normal line and the point (1, f(1)).

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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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