anonymous
  • anonymous
Prove that :-
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
|dw:1378466370733:dw|
ash2326
  • ash2326
@Tutor.Stacey Do you know the expansion of sin x?
ash2326
  • ash2326
*power series expansion

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anonymous
  • anonymous
yes
anonymous
  • anonymous
Actually Ignoring the limit and rearranging the equation gives you sinx = x. That's only true when x = 0. The only reason the limit exists in the original equation is because you cannot divide by zero.
anonymous
  • anonymous
am I correct?
anonymous
  • anonymous
just needed to give an explanation on this...
ash2326
  • ash2326
I'm not sure we can figure it out like that sin x =x cause that would be 0/0 an indeterminate form
anonymous
  • anonymous
:O
ash2326
  • ash2326
The idea is that when x approaches 0 either from left side or right side x=0+h or x=0-h where h is infinitesimally close to 0 but NOT 0 In that case sin x is approximately equal to x, so that \[\lim_{x\to 0}\frac{\sin x }{x} =1\]
anonymous
  • anonymous
Ah, I see!
ash2326
  • ash2326
You can verify this, take sin (0.05) 0.05 in radians, use your calculator and you'll see that it's around 0.05
ash2326
  • ash2326
Aha check this out https://www.google.com/search?q=sin(0.05)&oq=sin(0.05)&aqs=chrome..69i57.3668j0&sourceid=chrome&ie=UTF-8
ash2326
  • ash2326
how ever as x becomes larger this will not be the case and then it'll follow \[\sin x < x\]
anonymous
  • anonymous
This is what Archie said previously: To prove this I would set up a unit circle and find the area of the triangle with legs sin(x) and cos(x), area of the sector of angle x, and area of triangle with legs 1 and tan(x). Now rearrange and set up and equation with these which will lead you to the fact that 1≤limx→0sinxx≤1
ash2326
  • ash2326
you know in fact \[-1\le \sin x \le 1\] this is true for all x belonging to real numbers, I'm not sure how it'd help
anonymous
  • anonymous
Well- anyways, thanks for your help though! [:
ash2326
  • ash2326
@Tutor.Stacey So you have understood my explanation, haven't you?
anonymous
  • anonymous
Yes- kinda.
anonymous
  • anonymous
this is a Tiresome question, aye?
ash2326
  • ash2326
Nope, it's easy. But we should know where we should head
anonymous
  • anonymous
right!
ash2326
  • ash2326
Do you want to know another way of proving this?
anonymous
  • anonymous
Ash, thanks anyways for ur assistance. nd btw nty not right now since I need to get some sleep its really late....
ash2326
  • ash2326
Cool Tutor
anonymous
  • anonymous
*yawns* <.<
ash2326
  • ash2326
Night night
anonymous
  • anonymous
hehe, I'm not a tutor though.
anonymous
  • anonymous
just like calling myself Tutor Stacey... x_x
ash2326
  • ash2326
ha ha, now you sleep Stacey :P
anonymous
  • anonymous
Yes! xD

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