Proof using delta-epsilon method: Is it correct?

[DigitalSplendid]

The answer to the exercise has E/5 instead of E/8.

 

[blamocur]

I don't understand your derivations, but the answer to the exercise, i.e. $\epsilon/5$, looks wrong. To see that pick a small $\epsilon$, e.g. 0.001, compute values of $\lambda^2+\lambda$ for $\lambda = 3\pm \frac{\epsilon}{5}$ and check whether they fit in the $(12-\epsilon,12+\epsilon)$ interval.

 

[jonah2.0]

Beer induced hack reaction follows.

View attachment 39125

The answer to the exercise has E/5 instead of E/8.

Watch the whole video, especially the quadratic examples (last two).

 

[DigitalSplendid]

Beer induced hack reaction follows.


Watch the whole video, especially the quadratic examples (last two).

Thanks!

 

[DigitalSplendid]

I don't understand your derivations, but the answer to the exercise, i.e. $\epsilon/5$, looks wrong. To see that pick a small $\epsilon$, e.g. 0.001, compute values of $\lambda^2+\lambda$ for $\lambda = 3\pm \frac{\epsilon}{5}$ and check whether they fit in the $(12-\epsilon,12+\epsilon)$ interval.

Thanks! I have revised my earlier solution. Would especially appreciate to know if it is okay to assume x+4 <= 8 when strictly it is x+4< 8. I have solved assuming both.

 

[blamocur]

Would especially appreciate to know if it is okay to assume x+4 <= 8 when strictly it is x+4< 8.

I don't understand why it matters. Moreover, I don't understand how you deduce that $|\lambda-3| > 8\epsilon$ from the assumption that $|\lambda+4| < 8$.
To be able to help I'd need to see two things:
- The exact statement of the problem you are solving
- Step by step reasoning leading to your answer; numbering those steps would make the discussion easier and more productive.

 

[DigitalSplendid]

I don't understand why it matters. Moreover, I don't understand how you deduce that $|\lambda-3| > 8\epsilon$ from the assumption that $|\lambda+4| < 8$.
To be able to help I'd need to see two things:
- The exact statement of the problem you are solving
- Step by step reasoning leading to your answer; numbering those steps would make the discussion easier and more productive.

Sorry!

It is x - 3 and not delta - 3. Similarly x + 4 and not delta + 4.

 

[DigitalSplendid]

I don't understand your derivations, but the answer to the exercise, i.e. $\epsilon/5$, looks wrong. To see that pick a small $\epsilon$, e.g. 0.001, compute values of $\lambda^2+\lambda$ for $\lambda = 3\pm \frac{\epsilon}{5}$ and check whether they fit in the $(12-\epsilon,12+\epsilon)$ interval.

Sorry!

It is x - 3 and not delta - 3. Similarly x + 4 and not delta + 4.

Solving problem no. 32.

 

[blamocur]

After finding the book online to double-check that 1.4.1 is the standard delta-epsilon definition of limits I still believe that their answer is wrong and yours, i.e, $\delta < \epsilon/8$, is correct. They seem to assume that $|x+4|<5$, probably by confusing $x$ with $\delta$. Things happen