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Question

limx0xcosx+2sinxx2+tanx


Solution

limx0xcosx+2sinxx2+tanx

Dividing numerator and denominator by x

=limx0cosx+2sinxxx+tanxx

=limx0cosx+limx02sinxxlimx0x+limx0tanxx

=cos0+2 limx0sinxxx+limx0tanxx

=1+20+1=3              [limx0sinxx=1,limx0tanxx=1]

=3

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