Find the limit... ?

Find the limit... ? please THANK YOUenter image source here

1 Answer
sente
Jan 15, 2017

lim_(x->oo)(sqrt(x^4+2x^3)-(x^2+x))=-1/2

Explanation:

lim_(x->oo)(sqrt(x^4+2x^3)-(x^2+x))

=lim_(x->oo)((sqrt(x^4+2x^3)-(x^2+x))(sqrt(x^4+2x^3)+(x^2+x)))/(sqrt(x^4+2x^3)+(x^2+x))

=lim_(x->oo)(((x^4+2x^3)-(x^4+2x^3+x^2)))/(sqrt(x^4+2x^3)+x^2+x)

=lim_(x->oo)(-x^2)/(sqrt(x^4+2x^3)+(x^2+x))

=lim_(x->oo)-1/(sqrt(1+2/x)+1+1/x)

=-1/(sqrt(1+2/oo)+1+1/oo)

=-1/(sqrt(1+0)+1+0)

=-1/2

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