Chapter 4.1, Problem 14AYU

Explain what the notation $\underset{x\to \infty }{\lim }f\left(x\right)=-\infty$ means.

To determine

To explain: ${\underset{}{\lim }}_{x\to \infty }f\left(x\right)=-\infty$

Answer to Problem 14AYU

$\lim x\to \infty f\left(x\right)=-\infty \text{ is explained}$.

Explanation of Solution

Given:

${\underset{}{\lim }}_{x\to \infty }f\left(x\right)=-\infty$

$y=f\left(x\right)=a_n{x}^n$

Here $a_n<0$

If $a_n<0$, for increasing values of $x$ approaching to positive infinity value of limit of $y=f\left(x\right)$ decreases in the negative direction equals negative infinity.