Use the graph of f(x) to investigate the limit

  • Thread starter nycmathguy
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  • #1
Homework Statement:
Use the graph of f(x) to investigate the limit.
Relevant Equations:
Piecewise-defined Function
Use the graph to investigate the limit of f(x) as x tends to c at the number c.

See attachments.

Based on the graph of f(x), here is what I did:

lim (2x + 1) as x tends to 0 from the left is 1.

lim (2x) as x tends to 0 from the right is 0.

LHL does not equal RHL.

I conclude the limit of f(x) as x tends to c at the number c (c = 0) does not exist.
 

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Answers and Replies

  • #2
berkeman
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Homework Statement:: Use the graph of f(x) to investigate the limit.
Relevant Equations:: Piecewise-defined Function

I conclude the limit of f(x) as x tends to c at the number c (c = 0) does not exist.
Um, one of your piecewise continuous definitions includes and "=" sign...
 
  • #3
36,709
8,708
I conclude the limit of f(x) as x tends to c at the number c (c = 0) does not exist.
Looks good to me.
 
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Likes Delta2 and nycmathguy
  • #4
Um, one of your piecewise continuous definitions includes and "=" sign...
Meaning?
 
  • #5
Looks good to me.

That's what I thought. I may post one more like this involving a piecewise function in terms of 3 pieces. Let me think about it.
 
  • #6
36,709
8,708
Um, one of your piecewise continuous definitions includes and "=" sign...
Meaning?
Doesn't matter whether one or both or neither of the function definitions has an = in it. The one-sided limits you found are correct, and your conclusion that the two-sided limit doesn't exist is also correct.

Well done.
 
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Likes nycmathguy and berkeman
  • #7
Doesn't matter whether one or both or neither of the function definitions has an = in it. The one-sided limits you found are correct, and your conclusion that the two-sided limit doesn't exist is also correct.

Well done.

Beautiful. I may post one more but this time, the piecewise function will be three pieces. Stay tune.
 

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