Tuesday, February 27, 2018

Find the limit without using L'Hopital's rule limxto0(xtanx)/(xtanx).


I solved it with L'Hopital's rule but I want to find out how can I solve it without using L'Hopital's rule.


Answer



limx0xtanxxtanx

=limx0(xxtanxtanxxtanx)
=limx0(1tanx1x)
=limx0(cosxsinx1x)
=limx0(cosxxsinxx1x)
=limx0(cosxsinxx1x1x)
=limx0(1x1x)
Because, limx0cosx=1  and  limx0sinxx=1
=0


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