Math Problem Statement

Which of the following is not an indeterminate power? Question 2 Select one: 0^0 cross out ∞^0 cross out 0^∞ cross out 1^∞

Solution

The expression that is not an indeterminate form is 1^∞.

Here's a breakdown of each option:

  1. 0^0: Indeterminate, as it can be argued to be either 0 or 1 depending on the context.
  2. ∞^0: Indeterminate, because it depends on how the limits approach infinity.
  3. 0^∞: Indeterminate, since it can lead to different results depending on the function approaching 0 and ∞.
  4. 1^∞: This evaluates to 1, so it is not indeterminate.

Would you like further explanations on any of these concepts? Here are some related questions:

  1. Why is 000^0 considered indeterminate in some contexts?
  2. How does the concept of limits apply to 0∞^0?
  3. Can you provide examples where 00^∞ is used in calculus?
  4. In what scenarios might 11^∞ be encountered?
  5. What are other common indeterminate forms in calculus?

Tip: Always consider the context of limits when determining if an expression is indeterminate.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Limits
Indeterminate Forms
Exponential Functions

Formulas

-

Theorems

Limits involving indeterminate forms

Suitable Grade Level

Grades 11-12