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Question

Evaluate: limx0(2x+22x+23x3)1x

A
4
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B
332
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C
38
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D
2
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Solution

The correct option is A 4
l=limx0(2x+22x+23x3)1x

Taking loge on both sides

logel=limx01xloge(2x+22x+23x3)

logel=limx01(2x+22x+23x3).(2x+22x(2)+23x(3)3)loge(2)limx0(1) (By Hospital Rule)

logel=[1+2(1)+3(1)]3loge2

logel=2loge2

logel=loge22

l=4

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