Question

Which of the following are indeterminate forms?
A. \(0^0\),
B. \(1^\infty\),
C. \(\infty^0\),
D. \(0\times\infty\), E. \(1\cdot\infty\).

• A. A and E Only
• B. A, B, C Only
• C. A, B, C, E Only
• D. A, B, C, D Only

Hint:

Common indeterminate forms include \(0^0\), \(1^\infty\), \(\infty^0\), \(0\cdot\infty\), \(\frac{0}{0}\), and \(\frac{\infty}{\infty}\).

Answer 1

The Correct Option is D

Concept:
Indeterminate forms are forms whose limiting value cannot be directly decided.

Step 1: Check given forms. \[ 0^0 \] is indeterminate. \[ 1^\infty \] is indeterminate. \[ \infty^0 \] is indeterminate. \[ 0\times\infty \] is indeterminate.

Step 2: Check \(1\cdot\infty\). \[ 1\cdot\infty=\infty \] This is not an indeterminate form. Therefore, the indeterminate forms are: \[ A,B,C,D \] \[ \therefore \text{Correct Answer is (D)} \]