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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.
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).