# What is the equation of the line that is normal to #f(x)= -xsin^2x# at # x=(4pi)/3 #?

The line intersects the function at:

To find the slope of the normal line, first find the slope of the tangent line by differentiating the function. We'll need first the product rule, then the chain rule.

So the slope of the tangent line is:

The normal line is perpendicular to the tangent line, so their slopes will be opposite reciprocals. Thus, the slope of the normal line is:

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The equation of the line that is normal to f(x) = -xsin^2x at x = (4pi)/3 is y = -3sqrt(3) - (4pi/3)(sqrt(3)/2) + (sqrt(3)/2)x.

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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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