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Answer 1 · 2017-04-19T09:48:51

#3/2#

I edited your question, so I hope that this is the limit you are interested in.

#lim_(x to 0)(xe^x-ln(1+x))/(x^2)#

By l'H#hat("o")#pital's Rule (0/0),

#=lim_(x to 0)(e^x+xe^x-1/(1+x))/(2x)#

By l'H#hat("o")#pital's Rule (0/0) again,

#=lim_(x to 0)(e^x+e^x+xe^x+1/(1+x)^2)/(2)=(1+1+0+1)/2=3/2#

I hope that this was clear.