Question

`A= lim_"x->oo" sqrt((x^2+4)/(x+4))` `B=lim_"x->oo" sqrt((x^2+5)/x^3)` Find `A and B` ?

Answer 1

See below

Explanation:

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

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

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

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

`= oo`

`lim_ (x-> oo) sqrt((x^2+5)/x^3)`

`= lim_ (x-> oo) sqrt(1/x + 5/x^3)`

`= sqrt(lim_ (x-> oo) 1/x + lim_ (x-> oo) 5/x^3)`

`= sqrt 0`

`= 0`

Answer 2

`oo` and `0`

Explanation:

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

`lim_ (x-> oo) sqrt((x^2+5)/x^3) = sqrt(lim_ (x-> oo)(x^2)/(x^3)(1+5/x^2)) = 0`

Answer 3

`oo, 0`

Explanation:

`A= lim_"x->oo" sqrt((x^2+4)/(x+4))`

`= lim_"x->oo" sqrt((x+4/x)/(1+4/x))`

`=lim_"x->oo" sqrt(x/1) = oo`

`B=lim_"x->oo" sqrt((x^2+5)/x^3)`

`= lim_"x->oo" sqrt((1+5/x^2)/x)`

`=lim_"x->oo" sqrt(1/x) = 0`