# How do you solve the differential equation given #f''(x)=sinx#, f'(0)=1, f(0)=6?

Integrating gives us:

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To solve the differential equation f''(x) = sin(x) with initial conditions f'(0) = 1 and f(0) = 6, you can integrate sin(x) twice to find f(x). After integrating sin(x) twice, you will obtain an expression for f(x) with two arbitrary constants. Then, apply the initial conditions f'(0) = 1 and f(0) = 6 to determine the values of these constants.

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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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