Use Graph to Determine Limit: Calculating Limits with Piecewise Functions

• nycmathguy
In summary, the limit of the piecewise function as x tends to 1 is 2, as determined by the graph and confirmed by calculating the limits from the left and right. The limit of f(x) is also 2.
nycmathguy
Summary:: Graphs and Limits

Use the graph to determine the limit of the piecewise function as x tends to 1.

Let me see.

lim of (-x + 3) as x-->1 from the left is 2.

lim of (2x) as x-->1 from the right is 2.

I can safely say that the limit of f(x) as x tends to 1 from the left and right simultaneously is 1.

The limit of f(x) is 1.

Correct?

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nycmathguy said:
Summary:: Graphs and Limits

lim of (-x + 3) as x-->1 from the left is 2.

lim of (2x) as x-->1 from the right is 2.

I can safely say that the limit of f(x) as x tends to 1 from the left and right simultaneously is 1.

The limit of f(x) is 1.

Correct?

Typo ?

##\ ##

nycmathguy
BvU said:
Typo ?

##\ ##

Yes, big time typo. The limit is clearly 2 not 1. I was rushing through my first reply. Thank you for pointing out my typo. I will repost.

Delta2

Use the graph to determine the limit of the piecewise function as x tends to 1.

Let me see.

lim of (-x + 3) as x-->1 from the left is 2.

lim of (2x) as x-->1 from the right is 2.

I can safely say that the limit of f(x) as x tends to 1 from the left and right simultaneously is 2.

The limit of f(x) is 2.

P. S. Having fun with calculus so far. Hoping the excitement does not run out.

BvU and Delta2

1. What is a graph?

A graph is a visual representation of data that uses points, lines, and bars to show the relationship between two or more variables.

2. How can a graph be used to determine a limit?

A graph can be used to determine a limit by visually examining the behavior of a function as it approaches a specific value. The limit can be found by observing the trend of the function on the graph and determining the value it approaches as the input gets closer to the desired value.

3. What is the importance of using a graph to determine a limit?

Using a graph to determine a limit allows for a visual understanding of the behavior of a function, making it easier to interpret and analyze the data. It also provides a more accurate and precise determination of the limit compared to using numerical methods alone.

4. What are the key components of a graph used to determine a limit?

The key components of a graph used to determine a limit include the x and y-axis, the plotted points or function, and the point of interest where the limit is being evaluated.

5. How can a graph be used to determine if a limit exists?

A graph can be used to determine if a limit exists by observing the behavior of the function as it approaches the point of interest. If the function approaches a single value from both sides, the limit exists. If the function approaches different values from the left and right side, the limit does not exist.

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