Analyzing unbounded limits: mixed function | Limits and continuity | AP Calculus AB | Khan Academy

TL;DR

The video explains how to find the one-sided limits of a function and demonstrates two methods to approach the problem.

Transcript

• [Voiceover] So we're told that f of x is equal to x over one minus cosine of x minus two, and they ask us to select the correct description of the one-sided limits of f at x equals two. And we see that right at x equals two, if we try to evaluate f of two, we get two over one minus cosine of two minus two, which is the same thing as cosine of zer... Read More

Key Insights

• 0️⃣ f(2) is undefined because the denominator becomes zero.
• ☺️ The one-sided limits of f at x=2 can be determined by evaluating f(x) as x approaches 2 from the positive and negative directions.
• ☺️ Analyzing the properties of the cosine function helps determine the behavior of f as x approaches 2.
• 🚰 Creating a table and evaluating f(x) values near 2 can provide insights into the function's behavior.

Summary & Key Takeaways

• The function f(x) is given as x/(1-cos(x)-2), and the goal is to determine the one-sided limits of f at x=2.

• f(2) is undefined because the denominator becomes zero. Therefore, finding the limit as x approaches 2 is necessary.

• Using a table to analyze f(x) for values approaching 2 from positive and negative directions, it can be observed that the function approaches positive infinity.