Q. 42 - Calculus

Question

Calculate each limit in Exercises 35-80.

$\underset{x\to -\infty }{\lim }\left(5-2x+3x^3\right)$

Step-by-Step Solution

Answer

The limit of the expression is $\underset{x\to -\infty }{\lim }\left(5-2x+3x^3\right)=-\infty$.

Step 1. Given information.

We have:

$\underset{x\to -\infty }{\lim }\left(5-2x+3x^3\right)$

Step 2. Find the limits

The function is $\underset{x\to -\infty }{\lim }\left(5-2x+3x^3\right)$.

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

$$\begin{gathered} a=3,\hspace{0.17em}n=3 \\ =-\infty \hspace{0.17em} \end{gathered}$$