Q. 50 - Calculus

Question

Indeterminate forms: Identify which of the limit forms listed here are indeterminate. For each form that is not indeterminate, describe the behavior of a limit of that form.

${\infty }^{-\infty }.$

Step-by-Step Solution

Answer

Given limit form is not indeterminate and it will be always $\infty .$

Step 1. Given Information.

Given is a limit form: ${\infty }^{-\infty }.$

Step 2. Indeterminate forms available.

$$\begin{gathered} We have following 7 indeterminate forms available with us: \\ {\infty }^0, \infty -\infty , \frac{0}{0} , \frac{\infty }{\infty } , 0^0 , 0\times \infty , 1^{\infty }. \end{gathered}$$

Step 3. Determining the value of the limit form given.

Since, it is clear that it is not an indeterminate form.

As we know ${\infty }^{\infty } means infinity power infinity will be infinity.$

And we need to find $\frac{1}{{\infty }^{\infty }} which will be 0 as 1 divided by infinity will be 0.$

That's why the value of ${\infty }^{-\infty } will be 0.$