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Question

Evaluate: limx0e5x-e4xx


A

1

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B

2

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C

4

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D

5

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Solution

The correct option is A

1


Explanation for the correct answer:

Simplifying the equation to determinate form and applying the limits:

limx0e5x-e4xxlimx0e5x-1-e4x+1x[Adding-1+1inthenumerator]limx0e5x-1x-e4x+1xlimx05e5x-15x-4e4x+14x[Multiplyanddivide5infirsttermand4insecondterm]

Applying the limits

5×1-4×1limx0ex-1x=15-41

Thus, limx0e5x-e4xx=1

Therefore, the correct answer is option (A).


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