Q. 37 - 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.

$0^{\infty }$.

Step-by-Step Solution

Answer

Given limit form is not indeterminate and it will be always 0.

Step 1. Given Information.

Given a limit form: $0^{\infty }.$

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. 

Now, it's value will be 0 because as infinity is a very large value and when we increase the power of 0 it will be always equal to 0 whatever will be the power of 0. 

That's why, $0^{\infty } = 0.$