Q. 10 - Calculus

Question

Determine which of the given forms are indeterminate. For each form that is not indeterminate, describe the behavior of a limit of that form.

$0^1,0^0,0^{\infty },1^{\infty },{\infty }^1,{\infty }^0,{\infty }^{\infty }$

Step-by-Step Solution

Answer

The indeterminate forms are $0^0,1^{\infty },{\infty }^0,$and ${\infty }^{\infty }$

Step 1. Given Information

The given limits are $0^1,0^0,0^{\infty },1^{\infty },{\infty }^1,{\infty }^0,{\infty }^{\infty }$

Step 2. Identifying Indeterminate forms

$0^1$is non-indeterminate forms and is equal to zero.

$0^0$ is indeterminate forms of limit because 0 to the power 0 is undefined! 

$0^{\infty }$is  indeterminate forms .

$1^{\infty }$is equal to one because one is multiplied by infinity gives 1.

${\infty }^1$is undefined. when infinity is multiplied by any number, answer will be zero.

${\infty }^0$ is non-indeterminate forms  and is equal to one.

${\infty }^{\infty }$is indeterminate forms .