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Saturday, June 6, 2015

Problems : Limits

Problems for Indian Statistical Institute, Chennai Mathematical Institute, JEE Main and Advanced.
1.Evaluate:limx20+2x+33x2+4x3+38x4
2.Evaluate:limx(xx2+a2x4+a4)
3.Evaluate:limxx3{x2+x4+12x}
4.Evaluate:limxxcos2xx+sinx
5.Evaluate:limx[2log(3x)log(x2+1)]
6. Let Rn=2+2+2++2 (n square roots signs). Then evaluate limnRn
7. If an=(1+1n2)(1+22n2)2(1+32n2)3(1+n2n2)n, then evaluate limna1n2n
8.Evaluatelimxx2+xx2+1
9.limxπ2(sinx)tanx
10.limx0cosx1sin2x
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