Finding limits on a graph (if they exist)

Nicolas5150

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I have tried to the best of my knowledge to get the correct answers but I wanted to check with the community to see if there are any errors - I have a feeling one or two are incorrect since I left out the point (0,1) from any of the answers. If you could also explain as to why it is incorrect that would help immensely.
imgV2.jpg Thank you for the assistance in advance.
 
I have tried to the best of my knowledge to get the correct answers but I wanted to check with the community to see if there are any errors - I have a feeling one or two are incorrect since I left out the point (0,1) from any of the answers. If you could also explain as to why it is incorrect that would help immensely.
View attachment 3666 Thank you for the assistance in advance.

Perfect. Everything is correct.
Cheers!!
 
Perfect. Everything is correct.
Cheers!!

Though for (f), it is more accurate to say the limit is -∞. DNE is used to mean where the limit as x approaches a number from both the left and right hand sides do not approach the same y value. In this case, however, the function approaches -∞ from both sides.
 
Though for (f), it is more accurate to say the limit is -∞.

If the OP's course has provided a definition for the meaning of "limit = -∞", then I agree with you, Michael. :)

But, the response "DNE" is better for students who have yet to be introduced to infinite limits.



Nicolas:

By definition, a limit is always a Real number.

Hence, when a function increases or decreases without bound (as the inputs approach some number in the domain), then no limit exists because the function is not approaching a Real number.

When we see (or write) that a limit "is" ±infinity or "equals" ±infinity, the meaning should be understood that (1) the limit does not exist and (2) the function is increasing (or decreasing) without bound.

In other words, one would write "limit = -∞" only after a definition has been given for what mathematicians intend by saying that a limit "equals" negative infinity.

Cheers :cool:
 
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