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What is #f(x) = int 5e^(2x)-2e^x-x dx# if #f(4 ) = 1 #?

Answer 1

Christopher Agresta

# f(x) = 5/2e^(2x) - 2e^x - x^2/2 + 9 - 5/2e^8 + 2e^4 #

We have # f(x)=int5e^(2x)-2e^x-xdx #

Integrating gives us:

# f(x) = 5/2e^(2x) - 2e^x - x^2/2 + C #

We know #f(4)=1#, so

# 5/2e^8 - 2e^4 - 16/2 + C = 1 # # :. C = 9 - 5/2e^8 + 2e^4 #

Hence,

# f(x) = 5/2e^(2x) - 2e^x - x^2/2 + 9 - 5/2e^8 + 2e^4 #

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Answer 2

Christopher Allers

To find ( f(x) ) given ( f(4) = 1 ), integrate the function ( 5e^{2x} - 2e^x - x ) with respect to ( x ). Then, evaluate ( f(x) ) using the given condition ( f(4) = 1 ).

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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.