Question

Find the limit... ?

Find the limit... ? please THANK YOU

Answer 1

`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`