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Introduction to Limits: Part 2 Video Lecture | Crash Course for MAT

FAQs on Introduction to Limits: Part 2 Video Lecture - Crash Course for MAT

1. What is a limit in calculus?

Ans. A limit in calculus refers to the value that a function approaches as the input approaches a certain point or value. It represents the behavior of a function near a particular point and is denoted by the symbol lim.

2. How do you evaluate limits algebraically?

Ans. To evaluate limits algebraically, you can use various techniques such as direct substitution, factoring, rationalizing, and applying limit laws. These methods involve manipulating the given expression to simplify it and determine the limit.

3. Can a limit exist if a function is not defined at that point?

Ans. Yes, a limit can exist even if a function is not defined at that point. The concept of a limit focuses on the behavior of the function as it approaches a certain point, rather than the value of the function at that specific point. Therefore, a limit can exist even if the function is undefined at that point.

4. What is the difference between a one-sided limit and a two-sided limit?

Ans. A one-sided limit refers to the behavior of a function as the input approaches a certain point from either the left or the right side. It is denoted by using a positive or negative sign on the approaching value. On the other hand, a two-sided limit considers the behavior of the function as the input approaches the point from both the left and the right side.

5. How can you determine if a limit does not exist?

Ans. A limit does not exist if the function approaches different values as the input approaches a specific point from different directions. This can be observed through graphical analysis or by calculating the one-sided limits from both the left and the right side of the point. If these one-sided limits are unequal, the overall limit does not exist.

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Oct 10, 2025 Last updated

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