Question

I was going through one question and found out one inequality
that For x<0 , Sinx>x
But i didnt get it why. Can anyone help? :=|

Answer 1

We all know that -
sin|x| < |x|

multiply by -1 on both side
sin(- |x| ) > (- |x| )

& the rest is obvious :)

Answer 2

Oh ok , GOt it swimming through my neurons :D Thanks a Lot!

Answer 3

:)

Answer 4

oh wait lol now i started the question again and got confused again ,
how is Sin|x| <|x| ,@LastDayWork

Answer 5

There is a longer and more elaborate proof; but I personally prefer this one -
sinx = x (for x = 0)

now y=x has a constant slope (=1) but the slope of y=sinx is decreasing (from 1)
Hence, for all x >0 ; x > sinx

Tell me if that doesn't make sense & I'll give you another proof.

Answer 6

slope of y = sinx is decreasing ? i thought it was increasing and then decreasing? :S

Answer 7

Let f(x) = sinx
f'(x) = cosx

Now what do you think about the slope of f(x) ??

Answer 8

slope is cos x

Answer 9

right?

Answer 10

now it has maximum value at cosx=0 i.e. at x = Pi/2 , now thats all i got lol

Answer 11

Slope of f(x) = f'(x) = cos x
Now; at x = 0 ; y = sin x has slope = cos 0 = 1
For x > 0 ; sin x has slope = cos x < 1

Answer 12

oh right

Answer 13

Guess i got it lol thanx A LOT!!

Answer 14

:)

Answer 15

thx