Question

What is the limit of `(x^4 + x^5)` as x approaches infinity?

Answer 1

`\infty`

Explanation:

Write

`\lim_{x \rightarrow \infty} x^4 + x^5 = \lim_{x \rightarrow \infty} x^4 + \lim_{x \rightarrow \infty} x^5 = \infty + \infty = \infty`.
Or, you could think in this way. `x^5 +x^4` is a polynomial of degree 5. After the last root (the greater one), the function either increase or decrease without a bound. So the limit will always be `\infty` or `-\infty` depending on the sign