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Question:

limx→0 (e^x^2 - cosx)/sin^2x is equal to :

2

54

32

3

Solution:

limx→0ex2−cosxsin2x=limx→0ex2−cosxx2(sinxx)2=limx→01+x2+x42!−(1−x22!+x44!−.)x2(sinxx)2=1+12!=32