# Suppose that #f'(x) = 2x# for all #x#. What is #f(2)# if #f(1)=0#? What if #f(-2) = 3#?

Knowing the derivative, we should recognize that its definite integral generates an arbitrary constant:

so that

and

so that again,

and

It just means that both initial conditions are based on the same antiderivative (including its y-intercept).

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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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