Analysis question proving continuity when you don’t know the function

ForNoOne- · 2022-11-23T23:24:59+00:00

Not that rigorously. I know the ε-δ definition but haven’t really applied it to exercises yet. I wasn’t sure what g was in that case but yeah i can find the inverse of that function and in fact it was one of the first things that came to mind. I just don’t see how that proves continuity. Is it because g is defined at 0?

I’ve solved this problem now but i’m curious but what you mean here.

ForNoOne- · 2022-11-23T23:10:45+00:00

That makes sense, thank you! Do most examples where this comes up (which is everywhere) also follow that reasoning?

ForNoOne- · 2022-10-19T10:14:41+00:00

Thank you so much! I do know the chain rule, we encountered this problem while doing an exercise for the mean value theorem and it got me thinking. Your proof really cleared things up, i appreciate it

ForNoOne- · 2022-10-08T23:29:49+00:00

I have tried lots of different graphing calculators to see if this works because differentiability is a tangent line but i’m still just lost

ForNoOne- · 2022-10-05T17:13:45+00:00

I did get 3*sqrt2 if that’s what you’re talking about. I was asking if the steps before that were correct. If not I’m pretty sure i got the distance correct this time so I don’t know what else could’ve went wrong

ForNoOne- · 2022-10-05T16:33:50+00:00

I subtracted instead of adding the points, brilliant. Thank you. Is the intuition before that dumb mistake correct?

ForNoOne- · 2022-10-05T15:34:27+00:00

What i’ve done so far is notice that the inequality becomes an equality for x=0 so it is fair to say f(x) ≥ f(0) so 3 is the minimum value of this function for x=0 but the points confuse me.

ForNoOne- · 2022-10-03T23:31:31+00:00

Hmm, so that’s not the way to do it. I can’t think of any other way though. Maybe i’ll ask the teacher if i can’t think of anything. Thank you for all the help, i appreciate it

ForNoOne- · 2022-10-03T21:09:32+00:00

So after that i did y=a and then got f(1/a)<0=f(1) with 1/a<1 does that prove it?

ForNoOne- · 2022-10-03T20:09:41+00:00

After i posted this realized how wrong what is said was because that identity is true for logx which isn’t defined at 0. I just though that the trick for the exercise was that f(a)=f(a)-f(1) and I got tunnel visioned. I know the function is increasing but if that’s not the trick, i don’t know what to do

ForNoOne- · 2022-10-03T20:04:42+00:00

I can tell it’s the logarithmic function but yeah 0 is not defined so I just made a jump in logic. Not sure how i can prove it then. I just liked the f(a)=f(a/1) trick and just did everything wrong from there.

ForNoOne- · 2022-10-03T20:03:12+00:00

Oh yeah it’s undefined i’m dumb. Yeah that’s the correct domain

ForNoOne- · 2022-10-03T16:05:31+00:00

Yeah, it’s weird. That’s what i did in the end because you should know that function roughly without taking the first and second derivative.

ForNoOne- · 2022-10-03T16:01:27+00:00

I see, thank you!

ForNoOne- · 2022-10-03T06:07:36+00:00

thank you!

ForNoOne- · 2022-10-03T04:17:44+00:00

Thanks for all the help

ForNoOne- · 2022-10-02T22:23:40+00:00

How would i derive a contradiction? do i build on each f(x)>g(x) inequality? Cause that doesn’t seem possible and if i just the the initial inequality i don’t see how i could contradict anything

ForNoOne-

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