Consider the function f(x) whose second derivative is f''(x)= 8x+4sin(x), if f(0)=3 and f'(0)= 4, what is f(3)?
f(3)= 63- 4sin 3
The answer is obvious.
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To find f(3), you first need to find the first derivative of f(x) using the given information about f'(0) and f''(x). Then, integrate the first derivative to find f(x). Finally, plug in x=3 to find f(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.
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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