Q.8 - 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.

$\infty ·\infty 0·\infty 5·\infty 5·0 0.0$

Step-by-Step Solution

Answer

The indeterminate forms are $0·\infty and 5·\infty$

Step 1. Given Information

The given limits are $\infty ·\infty 0·\infty 5·\infty 5·0 0.0$

Step 2. identifying Indeterminate forms

$\infty ·\infty$ is Non-Indeterminate Forms for Limits because the result is also infinity.

$0·\infty$ is -Indeterminate Forms for Limits because Infinity is an undefined number (having no finite value), multiplying Infinity by Zero results in an undefined value. 

$5·\infty$ is -Indeterminate Forms for Limits Infinity is not considered a number, so infinity times three is technically undefined or no answer, because infinity is not necessarily a number.

$5·0$ is Non-Indeterminate Forms for Limits because any number multiplied by zero is zero.

$0·0$ multiplying by zero always gives zero,