Saturday, July 6, 2019

calculus - Find limlimitsxto0fraclogleft(cosxright)x2 without L'Hopital



limx0log(cosx)x2



I've been triyng to:




  1. show $\displaystyle -\frac{\pi}{2}


  2. find a function so that f(x)<log(cosx)x2 and limx0f(x)=12





And then apply the squeeze principle, but haven't managed any of these.


Answer



HINT:



log(cosx)x2=log(cos2x)2x2=12log(1sin2x)sin2x(sinxx)2


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