All Flashcards
Define a limit.
The y-value that a function, (f(x)), approaches as (x) gets closer to a specific value.
What does the limit of a function describe?
The function's behavior as the input approaches a certain value, not necessarily the value at that point.
Explain the meaning of ( \lim_{x \to a} f(x) = C ).
As (x) gets closer to (a), (f(x)) gets closer to (C).
How do you find the limit of a function numerically using a table?
Create a table of values as (x) approaches the target value from both sides. Observe the trend of (f(x)) to determine the limit.
How do you evaluate a limit graphically?
Examine the graph as (x) approaches the target value from both sides. The y-value that the function approaches is the limit.
What is the first step in evaluating a limit?
Substitute the value that (x) is approaching into the function.
Explain the concept of a limit.
A limit describes what value a function approaches as the input approaches a certain value, without necessarily reaching it.
Why is it important to consider approaching from both sides when evaluating a limit?
The limit exists only if the function approaches the same value from both the left and the right.
What is the difference between the limit of a function at a point and the function's value at that point?
The limit describes the function's behavior near the point, while the function's value is what the function equals at the point. They may not always be the same, especially with discontinuities.