Squeeze theorem exercise example  Limits  Differential Calculus  Khan Academy  Summary and Q&A
TL;DR
The video explains how to create a compound inequality and uses the squeeze theorem to find the limit of a function.
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 xvalues 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 xvalues.
Summary & Key Takeaways

The video demonstrates how to create a compound inequality that orders the values of three functions for xvalues 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 xvalues.

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.