# What is the equation of the line that is normal to #f(x)=sin^2x+e^xcotx # at # x=pi/3#?

It helps to know some trig derivatives:

First, take the derivative of

Simplify:

Plug in

That's the slope of the tangent line but we need the slope perpendicular to that which is simply the negative reciprocal.

We also need the point at

Now we can use point-slope form to find the equation of the normal line:

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

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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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- What is the instantaneous velocity of an object with position at time t equal to # f(t)= (1/(t-4),sqrt(5t-3)) # at # t=2 #?

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