Q. 14 - Calculus

Question

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

Step-by-Step Solution

Answer

(a) The limit $\infty +\infty$ is infinity and is a large number.

(b) The limit $\infty ·\infty$ is infinity and is a large number.

(c) The limit ${\infty }^1$  is infinity and is a large number.

Step 1. Given Information

The given limits are $\infty +\infty ,\infty ·\infty$and ${\infty }^1$

Part (a) Step 1. The limit ∞ + ∞

The limit of the form $\infty +\infty$ is non-indeterminate form and it gives a very large number.

Part(b) Step 1. The limit ∞ · ∞

The infinity multiplied by infinity is infinity which is a large number.

Part (c) Step 1. The limit ∞ 1

${\infty }^1=\infty$ because any number raised power 1 is itself the number.