songoku's latest activity
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Ssongoku reacted to PeroK's post in the thread Limit of piecewise function using epsilon delta with
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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... -
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!
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Ssongoku reacted to Gavran's post in the thread Limit of piecewise function using epsilon delta with Like.
I have used an online graphing calculator tool and I have found that $$ \delta=|\sqrt[3]{8+\epsilon}-2| $$. I am doubtful about finding...
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Ssongoku reacted to FactChecker's post in the thread Limit of piecewise function using epsilon delta with Like.
No. You only need to prove that there exists a positive delta that satisfies the requirements. You don't need to say anything more about...
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Ssongoku reacted to BvU's post in the thread Limit of piecewise function using epsilon delta with Like.
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Ssongoku reacted to PeroK's post in the thread Limit of piecewise function using epsilon delta with Like.
In this case, you might be able to calculate which one is the minimum. In general, however, you just need to show that such a delta...
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Ssongoku reacted to FactChecker's post in the thread Limit of piecewise function using epsilon delta with Like.
Good work. You don't need to know what it is, as long as you know it is positive and small enough. Just set ##\delta_1 = \min(...