# What is the slope of the line normal to the tangent line of #f(x) = cos(2x)*sin(2x-pi/12) # at # x= pi/3 #?

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To find the slope of the line normal to the tangent line of ( f(x) = \cos(2x) \cdot \sin\left(2x - \frac{\pi}{12}\right) ) at ( x = \frac{\pi}{3} ), we first need to find the derivative of the function ( f(x) ) and evaluate it at ( x = \frac{\pi}{3} ) to get the slope of the tangent line. Then, we find the negative reciprocal of this slope to get the slope of the normal line. Finally, we can plug in the value of ( x = \frac{\pi}{3} ) into the function to find the corresponding y-coordinate on the curve.

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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.

- What is the instantaneous velocity of an object moving in accordance to # f(t)= (2sin(2t+pi),tcos2t) # at # t=pi/3 #?
- What is the equation of the line normal to #f(x)=x^2+8x - 12# at #x=3#?
- What is the equation of the tangent line of #f(x) =x^2-x+4# at #x=2#?
- What is the equation of the line normal to #f(x)=3x^2 -5x +1 # at #x=-3#?
- What is the equation of the line that is normal to #f(x)= (2x-2)e^(2x-2) # at # x= 1 #?

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