Squeeze theorem exercise example | Limits | Differential Calculus | Khan Academy | Summary and Q&A

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June 18, 2015
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Squeeze theorem exercise example | Limits | Differential Calculus | Khan Academy

TL;DR

The video explains how to create a compound inequality and uses the squeeze theorem to find the limit of a function.

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Questions & Answers

Q: How do you create a compound inequality that orders the values of three functions?

To create a compound inequality, compare the values of the three functions for the given x-values near 2. Use the graph to determine the order of the functions and write f(x) ≤ g(x) ≤ h(x).

Q: What are the definitions of f(x), g(x), and h(x)?

f(x) = 2x times the square root of x minus 1 minus 1, g(x) is a rational expression, and h(x) = e to the x minus 2.

Q: How is the squeeze theorem used in this analysis?

The squeeze theorem is used to find the limit as x approaches 2 of the three functions. By comparing the limits, it is determined that the value of the limit is equal to 1.

Q: Why does g(x) approach 1 based on the graph?

Since f(x) and h(x) both approach 1 as x approaches 2, g(x) must also approach 1. This is because g(x) is sandwiched between f(x) and h(x) for the given x-values.

Summary & Key Takeaways

  • The video demonstrates how to create a compound inequality that orders the values of three functions for x-values near 2.

  • The functions f(x), g(x), and h(x) are compared, and it is concluded that f(x) ≤ g(x) ≤ h(x) for the given x-values.

  • The definitions of f(x), g(x), and h(x) are provided, and the squeeze theorem is used to find the limit as x approaches 2.

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