Question

Find the limit I need the answer for this question

Answer 1

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

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

Then, replace each variable for infinity.

$(\frac{\frac{2}{\infty^3}-\infty}{\frac{3}{\infty^2}+1})^3=(\frac{0-\infty}{0+1})^3=(-\infty)^3=\infty$

As you can observe, the limit is still undetermined.

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