Q. 40 - Calculus

Question

Calculate each limit in Exercises 35-80.

$\underset{x\to \infty }{\lim }\left(x^4-x^5\right)$

Step-by-Step Solution

Answer

The limit of the function is $\underset{x\to \infty }{\lim }\left(x^4-x^5\right)=-\infty$.

Step 1. Given information.

We have:

$\underset{x\to \infty }{\lim }\left(x^4-x^5\right)$

Step 2. Find the limits.

The function is $\underset{x\to \infty }{\lim }\left(x^4-x^5\right)$.

Apply infinity property: $\underset{x\to \infty }{\lim }\left(a{x}^n+\cdots +bx+c\right)=-\infty ,\hspace{0.17em}a<0,\hspace{0.17em}\mathrm{n}\hspace{0.17em}\mathrm{is}\hspace{0.17em}\mathrm{odd}$

$$\begin{gathered} a=-1,\hspace{0.17em}n=5 \\ =-\infty \end{gathered}$$