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Question

Evaluate limh0x+hxh

A
12x
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B
1x
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C
2x
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D
None of these
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Solution

The correct option is A 12x
Method I
limh0x+hxh (00form)
=limh0x+hxh×x+h+xx+h+x
=limh0(x+h)xh(x+h+x)
=limh0hh(x+h+x)
=limh01x+h+x=12x
Method II
limh0x+hxh (00form)
Applying L'Hospital's rule [differentiating numerator and denominator w.r.t. h]
=limh012x+h01=12x

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