Wednesday, 5 February 2014

calculus - Limit: limxto2frac1x2cdotsinleft(fracx2x+2right)



Can someone help me understand how the solution for the following limit is 1/4?




I've been trying to solve it but I always end up in a 'dead end' with an
indetermination. If someone could help me, that would be awesome.




limx21x2sin(x2x+2)



Answer



Note that for x2



1x2sin(x2x+2)=sin(x2x+2)x2=sin(x2x+2)x2x+21x+2114=14




indeed



y=x2x+20sin(x2x+2)x2x+2=sinyy1


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