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What is #f(x) = int e^x dx# if #f(0)=-2 #?

Answer 1

#e^x -3#

We have, #f(x)=inte^xdx# which comes out to be #e^x +C# where #C# is the constant of integration. We also have #f(0)=-2#.Plugging in this value in the expression we derived earlier, we get #e^0 +C#=-2 or #C#=-2-1 which is -3. Thus,the expression comes out to be #e^x -3#

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Answer 2

Evelyn Agard

Given (f(x) = \int e^x , dx) and (f(0) = -2), we can find the value of (f(x)).

Using the properties of integrals, we know that the integral of (e^x) with respect to (x) is simply (e^x).

Thus, (f(x) = e^x + C), where (C) is the constant of integration.

To find (C), we use the given condition (f(0) = -2).

Substituting (x = 0) into (f(x)), we get (f(0) = e^0 + C = 1 + C).

Given that (f(0) = -2), we equate (1 + C) to (-2) and solve for (C).

(1 + C = -2)

(C = -3)

Therefore, (f(x) = e^x - 3).

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Answer from HIX Tutor

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.