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How do you find the antiderivative of #e^-x#?

Answer 1

#= - e^(-x) + C#

Let #" "# #u(x) = e^(-x) # #" "# # du(x) = - e^(-x)dx# #" "# #rArr - du(x) = e^(-x)dx# #" "# #" "# #inte^(-x)dx# #" "# #= int-du(x)# #" "# #=-u(x) + C" " C# is a constant #" "# #= - e^(-x) + C#

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Answer 2

Emily Ammerman

To find the antiderivative of ( e^{-x} ), you can use the fact that the antiderivative of ( e^{ax} ) with respect to ( x ) is ( \frac{1}{a}e^{ax} + C ), where ( a ) is a constant and ( C ) is the constant of integration. Therefore, for ( e^{-x} ), the antiderivative is ( -e^{-x} + C ).

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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.