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Question

Solve: limx01cosxx

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Solution

limx01cosxx
LHL=limh01cos(h)h
=limh01coshh
=limh011+2sin2h2h
=limh02sin2h2(h2)2h×(h2)2
=limh024×h=12×0=0
RHL=limh0+1cos(h)h
=limh0+1coshh
=limh0+11+2sin2h2h
=limh0+2sin2h2(h2)2h×(h2)2
=limh0+24×h=12×0=0
LHL=RHL=0
Hence limx01cosxx=0

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