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What is the slope of the line normal to the tangent line of #f(x) = xcotx+2xsin(x-pi/3) # at # x= (5pi)/8 #?

Answer 1

Aurora Alvarado

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Answer 2

Emma Aldridge

To find the slope of the line normal to the tangent line of ( f(x) = x \cot(x) + 2x \sin(x - \frac{\pi}{3}) ) at ( x = \frac{5\pi}{8} ), follow these steps:

Find the derivative of ( f(x) ) using the product rule and chain rule.
Evaluate the derivative at ( x = \frac{5\pi}{8} ) to get the slope of the tangent line.
Find the negative reciprocal of this slope to get the slope of the line normal to the tangent line.

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Answer from HIX Tutor

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.