Chapter 1.2, Problem 25E

To determine

To find: The value of limit.

Answer to Problem 25E

The limit is -2

Explanation of Solution

Given information: The expression is $y=\frac{\cos x-2x^3}{x^3}$

Calculation:

The given expression is:

  $y=\frac{\cos x-2x^3}{x^3}$

The limit as:

  $\begin{array}{c}\underset{x\to \infty }{\lim }y=\underset{x\to \infty }{\lim }\frac{\cos x-2x^3}{x^3}\\ =\underset{x\to \infty }{\lim }\frac{\cos x}{x^3}-2\\ =0-2\\ =-2\end{array}$

And

  $\begin{array}{c}\underset{x\to \infty }{\lim }y=\underset{x\to \infty }{\lim }\frac{\cos x-2x^3}{x^3}\\ =\underset{x\to \infty }{\lim }\frac{\cos x}{x^3}-2\\ =0-2\\ =-2\end{array}$

Therefore the required limit is -2.