Evaluate the following limits \lim_{x\to\infty}(\sqrt{x^2+4x+1}-x)

ankarskogC 2021-10-26 Answered
Evaluate the following limits
limx(x2+4x+1x)
limx(x2+4x+1x)
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komunidadO
Answered 2021-10-27 Author has 86 answers
We have to evaluate the limit
a) limx(x2+4x+1x)
=limxx2+4x+1xx2+4x+1+x×x2+4x+1+x
=limxx(4+1x)x(1+4x+1x2+1)
41+1=42=12
b) limx(x2+4x+1x)
pu x=-x
limx(x2+4x+1x)=limx(x24x+1+x)
=limxx24x+1+limxx
limxx2(14x+1x2}+
=+
limx(x2+4x+1x)=
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