`lim_(x->oo) (sqrt(x^4)+4x^3)/(7x^2 + 1)`
`lim_(x->00) (sqrt(x^4)+4 x^3)/(14 x)`
Factor out constants:
`lim_(x->oo) (sqrt(x^4)+4 x^3)/(14 x)`
Factor out constants:
`= 1/14 (lim_(x->oo) (4 x^3+sqrt(x^4))/x)`
The limit of a sum is the sum of the limits:
`= 1/14 (lim_(x->oo) sqrt(x^4)/x+4 (lim_(x->oo) x^2))`
Using the power law, write` lim_(x->oo) x^2 as (lim_(x->oo) x)^2`:
`= 1/14 (lim_(x->oo) sqrt(x^4)/x+4 (lim_(x->oo) x)^2)`
The limit of x as x approaches
is
:
`= 1/14 (lim_(x->oo) sqrt(x^4)/x+oo)`
Simplify radicals, `sqrt(x^4)/x = sqrt(x^2)`:
`= 1/14 (lim_(x->oo) sqrt(x^2)+oo)`
Using the power law, write `lim_(x->oo) sqrt(x^2) as sqrt(lim_(x->oo) x^2)`:
`= 1/14 (sqrt(lim_(x->oo) x^2)+oo)`
Using the power law, write `lim_(x->oo) x^2 as (lim_(x->oo) x)^2`:
`= 1/14 (sqrt((lim_(x->oo) x)^2)+oo)`
The limit of x as x approaches
is
:
`= oo`