Matematické Fórum

stuart clark

If $f'(0)=0$ and $f(x)$ is differntiable and increasing function

Then value of $\displaystyle \lim_{x\rightarrow 0}\frac{x\cdot f'(x^2)}{f'(x)}$ is

check_drummer · 11. 04. 2019 23:39

Hi, everything seems to me that it should be

Autor skryl část textu. Zobrazit/skrýt!

even for nonincreasing functions...

stuart clark · 14. 04. 2019 10:17

Thanks ↑ check_drummer:

but in answer, left side limit does not exists and right side limit $0$

byk7 · 15. 04. 2019 12:30

↑ stuart clark: Then there is a mistake in the answer key. Consider f(x)=x^3, then f'(x)=3x^2, f'(x^2)=3x^4 and
$\lim_{x\to0}\frac{x\cdot3x^4}{3x^2}=\lim_{x\to0}x^3=0$ .

stuart clark · 17. 04. 2019 11:07

Thanks ↑ byk7: got it.

Bati · 17. 04. 2019 11:55

↑ byk7:
what does it prove about the original limit??

byk7 · 17. 04. 2019 12:21

↑ Bati: nothing, it just demonstrates that ↑ stuart clark: 's answer is wrong.

Bati · 17. 04. 2019 13:26

↑ byk7:
it might not..for some fs

Andrejka3 · 17. 04. 2019 16:00

↑ Bati:
If I see a statement such as ↑ stuart clark: and there is a free variable (f), then I automatically consider it a shortcut of longer statement: (forall f) (the original statement).
Perhaps ↑ byk7: understants it the same way.

Bati · 17. 04. 2019 16:57

↑ Andrejka3:
yes, but what im saying that the answer in the key might be just poorly stated..but if it is actually true that there is a function for which the limit doesnt exist, its much mire interesting than saying for some f the limit is 0 (which is obvious).

Somebody should really solve this and end this discussion :)

stuart clark · 18. 04. 2019 13:03

Thanks to all members .Yes you all are right my answer is wrong

Matematické Fórum

#1 11. 04. 2019 10:47 — Editoval stuart clark (11. 04. 2019 10:48)

function and limit

#2 11. 04. 2019 23:39

Re: function and limit

#3 14. 04. 2019 10:17

Re: function and limit

#4 15. 04. 2019 12:30

Re: function and limit

#5 17. 04. 2019 11:07

Re: function and limit

#6 17. 04. 2019 11:55

Re: function and limit

#7 17. 04. 2019 12:21

Re: function and limit

#8 17. 04. 2019 13:26

Re: function and limit

#9 17. 04. 2019 16:00

Re: function and limit

#10 17. 04. 2019 16:57

Re: function and limit

#11 18. 04. 2019 13:03

Re: function and limit

Zápatí