# Is #f(x)=x-e^x/sinx# increasing or decreasing at #x=pi/3#?

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To determine if ( f(x) = \frac{x - e^x}{\sin(x)} ) is increasing or decreasing at ( x = \frac{\pi}{3} ), we need to analyze the sign of its derivative ( f'(x) ) at that point. The derivative of ( f(x) ) can be found using the quotient rule. After finding the derivative, evaluate it at ( x = \frac{\pi}{3} ). If ( f'(x) > 0 ), then ( f(x) ) is increasing at ( x = \frac{\pi}{3} ). If ( f'(x) < 0 ), then ( f(x) ) is decreasing at ( x = \frac{\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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