Question!!!

Question

Question!!!

anonymous · Answer

Answer!!!

diyadiya · Answer

Lol Wait!!

anonymous · Answer

I can't, lunch time!!!

anonymous · Answer

What I lack in mathematical know-how I make up for in speedy typing.

diyadiya · Answer

Find the points of discontinuity of f, where

mr.math · Answer

None!

diyadiya · Answer

Show..

mr.math · Answer

The limit of f(x) as x approaches 0 from the right is the same as from the left, both are 1.

diyadiya · Answer

What is
$$\lim_{x \rightarrow 0} \frac {\sin x }{x}$$

mr.math · Answer

$$\lim_{x\to 0^+}f(x)=\lim_{x\to 0^+}{\sin(x) \over x}=1=\lim_{x\to 0^-}f(x)=\lim_{x\to0^-}(x+1).$$

mr.math · Answer

It should be the opposite, I mean the - and +. Just a typo!

diyadiya · Answer

isn't 
$$\lim_{x \rightarrow 0^+} f(x)=\lim_{x \rightarrow 0^+}(x+1) ?$$

mr.math · Answer

Yep! That's what I just said.

turingtest · Answer

$$\lim_{x \rightarrow 0}{\sin x \over x}=1$$can be shown through L'hospitals rule, since you asked earlier.

diyadiya · Answer

Oh :)

diyadiya · Answer

ThankYou Mr.Math & TuringTest :)

mr.math · Answer

I wonder why Diya has a medal and I don't! :P

turingtest · Answer

who needs 'em?

diyadiya · Answer

Lol I'l definitely Give medals :) dw

mr.math · Answer

Lol, I don't! I'm just joking. It's worth wondering though :P

mr.math · Answer

This is the proof of the limit of sinx/x without using L'hopital's rule if you want: http://www.youtube.com/watch?v=Ve99biD1KtA

turingtest · Answer

yeah, that's the real way...

turingtest · Answer

one of them

diyadiya · Answer

Thanks I'll watch it 
But is it the same for cos(x)/x ?

anonymous · Answer

Good answer! I had to go back and find old notes on curve sketching because it's been a while and I couldn't remember the conditions of continuity ;) But nicely done.

mr.math · Answer

No, the limit of cosx/x as x goes to zero is infinity.

mr.math · Answer

Well $\pm \infty$ depends on which direction you're approaching from.

mr.math · Answer

$\pm \infty$.

diyadiya · Answer

Hm okay 
If you dont mind 
What about other Trigonometric Functions?

mr.math · Answer

You mean $\frac{\tan(x)}{x}$ for example?

diyadiya · Answer

Yes

mr.math · Answer

In the case of tanx/x, the limit is 1.

anonymous · Answer

because sin x /cos x = tan x

mr.math · Answer

You can derive the rest from the above actually.

mr.math · Answer

Or you can always apply L'Hopita's Ruel.

diyadiya · Answer

Lol Fine :) 
Thanks again!

mr.math · Answer

No problem!

anonymous · Answer

Why is diya thanking so many times ?

anonymous · Answer

it's vacation and we don't have any better things to do :P

diyadiya · Answer

Because i appreciate those people who helps me :)

mr.math · Answer

She has exams next year! :P

diyadiya · Answer

Yes^^