# What is #f(x) = int -3x-1 dx# if #f(2)=-3 #?

Clearly:

and

Now using the linearity of the integral:

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To find the function ( f(x) = \int_{-3}^{x} -3x - 1 , dx ) if ( f(2) = -3 ), you first need to find the antiderivative of ( -3x - 1 ), then evaluate it at ( x = 2 ) and solve for the constant of integration. Given that ( f(2) = -3 ), you can use this information to solve for the constant of integration.

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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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