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Question

Evaluate
L=limx01+x2cosxxtanx

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Solution

limx01+x2cosxxtanx is of 00 form.
Using L'Hospitals rule,we have
=limx02x+sinxxsec2x+tanx is of 00 form.
=limx02+cosx2xsec2xtanx+sec2x+sec2x
=limx02+cosx2xsec2xtanx+2sec2x
=2+10+2=32

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