Investigating A Limit Via Graph

In summary, the limit of f(x) as x approaches 2 from the left and right sides is 4, and the presence of a hole at (2, 4) does not affect the limit.
  • #1
nycmathguy
Homework Statement
Graphs and Limits
Relevant Equations
Quadratic and Piecewise Function
Use the graph to investigate

(a) lim of f(x) as x→2 from the left side.

(b) lim of f(x) as x→2 from the right side.

(c) lim of f(x) as x→2.

Question 18

For part (a), as I travel along on the x-axis coming from the left, the graph reaches a height of 4. The limit is 4. It does not matter if there is a hole at (2, 4), right?

For part (b), as I travel along on the x-axis coming from the right, the graph reaches a height of 4. The limit is 4. It does not matter if there is a hole at (2, 4), right?

For part (c), as I travel along on the x-axis coming from the left and right simultaneously, the graph reaches a height of 4. The limit is 4. It does not matter if there is a hole at (2, 4), right?

I conclude that the limit is 4.

You say?

I will answer 20 on a separate thread.
 

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  • #2
nycmathguy said:
Question 18

For part (a), as I travel along on the x-axis coming from the left, the graph reaches a height of 4. The limit is 4. It does not matter if there is a hole at (2, 4), right?
Correct. The left-side limit if 4, and the presence of a hole doesn't matter.
nycmathguy said:
For part (b), as I travel along on the x-axis coming from the right, the graph reaches a height of 4. The limit is 4. It does not matter if there is a hole at (2, 4), right?
Correct. The right-side limit if 4, and the presence of a hole doesn't matter.
nycmathguy said:
For part (c), as I travel along on the x-axis coming from the left and right simultaneously, the graph reaches a height of 4. The limit is 4. It does not matter if there is a hole at (2, 4), right?

I conclude that the limit is 4.
Yes, correct.
 
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Likes nycmathguy
  • #3
Mark44 said:
Correct. The left-side limit if 4, and the presence of a hole doesn't matter.
Correct. The right-side limit if 4, and the presence of a hole doesn't matter.
Yes, correct.

I finally get one right on my own.
 

FAQ: Investigating A Limit Via Graph

What is a limit?

A limit is a fundamental concept in calculus that represents the value a function approaches as its input approaches a certain value. It is denoted by the symbol "lim" and is used to describe the behavior of a function near a particular point.

How do you investigate a limit via graph?

To investigate a limit via graph, you can plot the function on a graph and observe the behavior of the graph near the point in question. You can also use a graphing calculator or online graphing tool to visualize the function and its behavior.

What are the key features to look for in a graph when investigating a limit?

When investigating a limit via graph, you should look for the overall shape of the graph, any discontinuities or breaks in the graph, and any points where the function approaches a certain value. You should also pay attention to the behavior of the graph as the input approaches the point in question.

How can you use a graph to determine if a limit exists?

If the graph of a function has a hole or a gap at the point in question, then the limit does not exist. However, if the graph approaches a specific value as the input approaches the point, then the limit exists. You can also use the formal definition of a limit to determine its existence.

Can a graph alone determine the exact value of a limit?

No, a graph alone cannot determine the exact value of a limit. A graph can only provide an estimate or approximation of the limit. To find the exact value, you would need to use other techniques such as algebraic manipulation or the formal definition of a limit.

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