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nycmathguy

Member

Registered: 2021-06-02

Posts: 53

Limit of Two-piece Function

Use a graph to investigate limit of f(x) as x tends to c at the number c.

Note: f(x) is a piecewise function.

Note: I did not use a graph of the given function.

Top portion of piecewise function: x^3 if x < -1
Bottom portion of piecewise function: x^2 - 1 if x > -1

at c = -1

Solution:

Find the limit of x^3 as x tends to -1 from the left.

(-1)^3 = -1

Find the limit of x^2 - 1 as x tends to -1 from the right.

(-1)^2 - 1

1 - 1 = 0

The LHL DOES NOT = RHL.

Thus, the limit of f(x) does not exist.

zetafunc

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Registered: 2014-05-21

Posts: 2,440

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Re: Limit of Two-piece Function

Your conclusion is correct, but the same comments I made on your other piecewise function thread also apply here so I suggest you read that first (it's the same kind of set-up, just with two pieces rather than three).

The question did ask for you to use a graph. So what do you think the graph looks like and in particular what do you think it looks like near x = -1?

nycmathguy

Member

Registered: 2021-06-02

Posts: 53

Re: Limit of Two-piece Function

Your conclusion is correct, but the same comments I made on your other piecewise function thread also apply here so I suggest you read that first (it's the same kind of set-up, just with two pieces rather than three).

The question did ask for you to use a graph. So what do you think the graph looks like and in particular what do you think it looks like near x = -1?

Read my reply to the other thread. I am now learning how to use this site. I first have to learn how to upload picture attachments before we can talk about graphs of functions. You are right in your comment. However, I want to take it easy as I make my way through the Ron Larson textbook. No need to rush. No need to panic. No exam to prepare for. Get it?