Q. 46 - 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.  

$\frac{0}{\infty }.$

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: $\frac{0}{\infty }$.

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, $\frac{0}{\infty } = 0\times \frac{1}{\infty } = 0\times 0 = 0.$

That's why it's value is 0.