Finding Limits with Graph of Oscillating function attached to other functions

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avanm

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I am not understanding Oscillating functions. I understand Oscillating functions do not have limits but what about if it borders another function. For example this graph I made. If you are trying to find the limit of the function from x->3+ is that limit DNE because the oscillating portions limit DNE?
Same goes from x->5- does the limit exists there?

Thank you if you can help!
 

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avanm said:
I am not understanding Oscillating functions. I understand Oscillating functions do not have limits but what about if it borders another function. For example this graph I made. If you are trying to find the limit of the function from x->3+ is that limit DNE because the oscillating portions limit DNE?
Same goes from x->5- does the limit exists there?

Thank you if you can help!
Click to expand...
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
 
Subhotosh Khan said:
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
Click to expand...

I’m stuck trying to figure out if the limx->3+ and the limx->5-

I tried to look into how oscillating functions work, realizing they don’t have limits. I am confused as my understand is weak, if this applies to the border between two functions drawn in my image attached.
 
avanm said:
I’m stuck trying to figure out if the limx->3+ and the limx->5-

I tried to look into how oscillating functions work, realizing they don’t have limits. I am confused as my understand is weak, if this applies to the border between two functions drawn in my image attached.
Click to expand...

I think ive figured it out, you can approach the limit from those specific one sided limits because they oscillating functions limits DNE, where as if I approached the limits I mentioned from the opposite one sided limits, they would have a value.
 
Continuous oscillating functions will certainly have a limit. After all, ALL continuous functions have a limit on its domain. Doesn't the function sin x have a limit everywhere? It Oscillates! Oscillating functions can even have limits at infinity. Can you draw one?
 
avanm said:
I think ive figured it out, you can approach the limit from those specific one sided limits because they oscillating functions limits DNE, where as if I approached the limits I mentioned from the opposite one sided limits, they would have a value.
Click to expand...
Both limits equal 3. In this case it does NOT matter if you are coming from the left or the right, the limits are 3. Don't you see that?
 
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