Question

How do you find `\lim _ { x \rightarrow \infty } \frac { x ( x + x ^ { 3} ) + 4x ^ { 4} } { 1- 2x ^ { 4} }`?

Answer 1

`lim_(xrarr oo) (x(x+x^3)+4x^4)/(1-2x^4)= color(blue)(-5/2)`#

Explanation:

`lim_(xrarr oo) (x(x+x^3)+4x^4)/(1-2x^4)`

`color(white)("XXX")=lim_(xrarr oo) (x^2+5x^4)/(1-2x^4)`

...after dividing numerator and denominator by `x^4`
`color(white)("XXX")=lim_(xrarroo) ((x^2)/(x^4)+5)/(1/(x^4)-2`

`color(white)("XXX")=lim_(xrarroo) (1/(x^2)+5)/(1/(x^4)-2`

`color(white)("XXX")=(0+5)/(0-2)`

`color(white)("XXX")=-5/2`