songoku's latest activity
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Ssongoku reacted to Greg Bernhardt's post in the thread Announcement Please welcome berkeman as PF Admin with
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I am thrilled and honored to announce that @berkeman has accepted a role as PF Admin! @berkeman has 20 impactful years at PF under his... -
Ssongoku replied to the thread Limit of piecewise function using epsilon delta.I am very sorry for late reply Thank you very much for all the help and explanation pasmith, PeroK, FactChecker, BvU, Gavran...
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Ssongoku reacted to FactChecker's post in the thread Limit of piecewise function using epsilon delta with Like.
Sorry, my mistake. I didn't realize that this example is different from the one in post #1. In this example, one function equation works...
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Ssongoku reacted to PeroK's post in the thread Limit of piecewise function using epsilon delta with Like.
That's not really how we are supposed to construct a proof here. Instead, for ##0<\epsilon <1##, we should let: $$\delta =...
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Ssongoku reacted to Gavran's post in the thread Limit of piecewise function using epsilon delta with Like.
The post #15 was my mistake. When ## x\to 2^- ## ## \sqrt[3]{8-\epsilon}-2\lt x-2\lt\sqrt[3]{8+\epsilon}-2 ## does not imply ##...
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Ssongoku reacted to PeroK's post in the thread Limit of piecewise function using epsilon delta with Like.
In general, for a right hand limit at ##a## you are looking for:$$a < x <a +\delta$$And not $$0<|x-a|< \delta$$PS I see this was in the...
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Ssongoku reacted to anuttarasammyak's post in the thread Limit of piecewise function using epsilon delta with Like.
Please find below the plots of my understanding the situation. I hope it is not wrong and has some meanings.
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Ssongoku reacted to FactChecker's post in the thread Limit of piecewise function using epsilon delta with Like.
I can't say with authority whether part 2 is required. I am not a "proof policeman". If part 1 had stated things differently, like...
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Ssongoku reacted to Gavran's post in the thread Limit of piecewise function using epsilon delta with Like.
## x-2\lt0 ## and ## \sqrt[3]{8+\epsilon}-2\gt0 ## implies that ## x-2\lt\sqrt[3]{8+\epsilon}-2 ## always holds so ##...
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Ssongoku reacted to PeroK's post in the thread Limit of piecewise function using epsilon delta with Like.
You calculated the bounds based on a two-sided limit. Even though you said you were doing a one-sided limit. That's why you ended up...
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Ssongoku reacted to PeroK's post in the thread Limit of piecewise function using epsilon delta with Like.
If you look at his calculations. For ##x > 2##, where the function is quadratic, he includes the case ##x < 2##. Similarly, when ##x...
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Ssongoku reacted to FactChecker's post in the thread Limit of piecewise function using epsilon delta with Like.
For two-sided continuity, the limits must be equal. On each side, that delta and any smaller, strictly positive, delta will do. So the...
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Ssongoku reacted to PeroK's post in the thread Limit of piecewise function using epsilon delta with Like.
Although, there should only be one ##\delta## in each set, as we are dealing with a one-sided limit. For example, for the righthand...
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Ssongoku reacted to FactChecker's post in the thread Limit of piecewise function using epsilon delta with Like.
You are done. You have proved that ##\delta \gt 0## exists which satisfies the requirement. You accidentally dropped the absolute...
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Ssongoku reacted to PeroK's post in the thread Limit of piecewise function using epsilon delta with Like.
The first number in each set is negative!