songoku's latest activity
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Ssongoku reacted to Gavran's post in the thread Limit of piecewise function using epsilon delta with
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I have used an online graphing calculator tool and I have found that $$ \delta=|\sqrt[3]{8+\epsilon}-2| $$. I am doubtful about finding... -
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(...
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Ssongoku reacted to PeroK's post in the thread Limit of piecewise function using epsilon delta with Like.
Alternatively, go back to the requirement that: $$|x^2 - 4| < \epsilon$$Now factorise the left hand side. That's the normal approach.
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Ssongoku reacted to PeroK's post in the thread Limit of piecewise function using epsilon delta with Like.
You need to establish ##\delta## for each ##\epsilon##. You should stay focused on ##|x -2|##.
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Ssongoku reacted to PeroK's post in the thread Limit of piecewise function using epsilon delta with Like.
You can do the two one-sided limits as separate calculations. The limit is ##L## if and only if both one-sided limits are ##L##.
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Ssongoku reacted to pasmith's post in the thread Limit of piecewise function using epsilon delta with Like.
You haven't told us the definition of f. You can assume \epsilon < 8 (a \delta which works for such an \epsilon will also work for any...
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Ssongoku replied to the thread Limit of piecewise function using epsilon delta.Is calculating the bounds based on one - sided limit like post #24? But in post#15, the delta you take is ##|\sqrt[3]{8+\epsilon}-2|##...
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Ssongoku replied to the thread Limit of piecewise function using epsilon delta.Ah my bad Oh ok, but how about something like this? That example is from textbook and there is part 2 of the working (to show that...
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Ssongoku replied to the thread Limit of piecewise function using epsilon delta.I am trying to but sorry I don't have idea how to continue without choosing a certain value for ##\delta##. What I practice up until now...
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Ssongoku replied to the thread Limit of piecewise function using epsilon delta.Then how to continue the proof? Let: ##\delta_1=\text{min}\{\sqrt[3] {8-\epsilon}-2, \sqrt[3] {8+\epsilon}-2\}##...
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Ssongoku replied to the thread Limit of piecewise function using epsilon delta.Wait, I don't need to choose which one is the minimum? But then when I want to prove it, what should I put as ##delta##? Oh I have to...
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Ssongoku replied to the thread Limit of piecewise function using epsilon delta.For left side limit ##(x\to 2^{-})##, the ##\delta=|\sqrt[3] {8+\epsilon}-2|## For right side limit, ##(x\to 2^{+})##, the...
