Limits: 9-x as x Approaches 4 = 5

In summary, the conversation discusses the process of finding delta and epsilon in order to prove a limit using the epsilon-delta definition. The speaker mentions using a Khan Academy video as a resource and requests guidance in finding these values. The conversation also touches on the importance of properly posting homework assignments in the designated section.
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Not An Einstein
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lim(9-x) as x->4 = 5
I thought I was supposed to do this:
9-4=5
5=5
But apparently I was supposed to use delta and epsilon?
I'm not sure how to find either of these. I know you find epsilon first but I'm really confused so if anyone knows just HOW to find it, that would be extremely helpful. Thank you.
 
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1. What is a limit in calculus?

In calculus, a limit is a fundamental concept that describes the behavior of a function as its input values approach a certain value. It is used to find the value that a function approaches as the input gets closer and closer to a particular value.

2. How do we solve limits in calculus?

To solve limits in calculus, we can use various techniques such as direct substitution, factoring, and rationalization. We can also use L'Hospital's rule, which states that for certain types of limits, we can take the derivative of the numerator and denominator separately to simplify the limit.

3. How do we interpret the notation "x approaches 4" in a limit?

The notation "x approaches 4" means that we are considering the behavior of a function as the input values get closer and closer to the value 4. This does not necessarily mean that the function will actually reach the value 4, but rather that it gets closer and closer to it.

4. What does the statement "9-x as x approaches 4 = 5" mean?

This statement means that as the input values of the function 9-x get closer and closer to 4, the output values approach the value 5. In other words, the limit of the function 9-x as x approaches 4 is equal to 5.

5. Why is it important to understand limits in calculus?

Limits are important in calculus because they allow us to solve problems involving rates of change and continuity. They also play a crucial role in the definitions and applications of derivatives and integrals, which are fundamental concepts in calculus.

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