Question

Find the limit I need the answer for this question

Answer 1

To solve this, divide each part by the x^3.

`\lim _(x\to-\infty)((2-x^4)/(3x+x^3))^3=\lim _(x\to-\infty)(\frac{(2)/(x^3)-(x^4)/(x^3)}{\frac{3x}{x^3^{}}+(x^3)/(x^3)})^3=\lim _(x\to-\infty)(((2)/(x^3)-x)/((3)/(x^2)+1))^3`

Then, replace each variable for infinity.

`(((2)/(\infty^3)-\infty)/((3)/(\infty^2)+1))^3=((0-\infty)/(0+1))^3=(-\infty)^3=\infty`

As you can observe, the limit is still undetermined.

Therefore, the limit of the given function does not exist when x tends to -infinity.