Q. 12 - Calculus

Question

Describe in terms of large and small numbers why it makes intuitive sense that limits of the form (a) $0^{\infty }$ (b) $\left(b\right)0^1$must equal 0.

Step-by-Step Solution

Answer

(a) $0^{\infty }=0$ and the number is small.

(b) $0^1=0$ and the number is small.

Step 1. Given Information

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

Part (a) Step 1. Sense of limits 0 ∞

By using $a^m=a\times a\times a...\times a$

$0^{\infty }=0\times 0\times 0\times ...upto infinity=0$

This number is small.

Part (b) Step 2. Sense of limits 0 1

We have $0^1=0$

This is also small.