Monday, 28 November 2016

calculus - Evaluating limxto0fracxsin(sinx)sin2xx6






Evaluate:
lim




I have been trying to solve this for 15 minutes but sin(sin(x)) part has me stuck.



My attempt:



I tried multiplying with x inside the \sin as \sin{(\frac{x\sin{x}}{x})}. No leads.



Answer



Use \sin(u)=u-\frac{u^3}{6}+\frac{u^5}{120}+o(u^6) (three times).


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