# What is #f(x) = int -sinx dx# if #f(pi/3) = -6 #?

where c is the constant of integration.

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To find ( \int -\sin(x) , dx ), integrate the function ( -\sin(x) ) with respect to ( x ).

[ \int -\sin(x) , dx = \cos(x) + C ]

Given that ( f(\frac{\pi}{3}) = -6 ), we can find ( C ) by substituting ( \frac{\pi}{3} ) into ( \cos(x) + C ) and equating it to ( -6 ).

[ \cos\left(\frac{\pi}{3}\right) + C = -6 ]

[ \frac{1}{2} + C = -6 ]

[ C = -6 - \frac{1}{2} = -\frac{13}{2} ]

So, ( f(x) = \cos(x) - \frac{13}{2} ).

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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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