Q. 40 - 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.

$\frac{\infty }{1}.$

Step-by-Step Solution

Answer

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

Step 1. Given Information.

$Given a limit form: \frac{\infty }{1}.$

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 $\infty$ always because whatever be the numerator but if denominator is 1 then it doesn't affect the value in the numerator. If denominator is 1 then it can be ignored and it's value will be equal to numerator as well.

That's why, $\frac{\infty }{1} = \infty .$