66Hint: Consider the function f(x)=x - sin x and prove that f is non decreasing for all x.
i m not able to prove > but i m getting x>=sinx!!!!
is the question correct??????
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5 Answers
66
1sir that's how i tried to solve the sum!
but what i wanna say is this
f(x)=x-sin x
f'(x)=1-cos x >or=0[at points where cos x =1]
also,f(0)=0-0=0
so we conclude that function is non-decreasing[not strictly increasing]
so,x>or=sinx
so, i feel that question might be incorrect!!!
1make the graph of y=x and y=Sinx.
from the graph you can clerly show that value of x is greater than Sinx.
1since 0 is in open interval in domain of x we canot include 0
but at 0 x=sinx
so x>sinx is incorrect if 0 is included
but if 0 is not included then we check for a no. slightly greater then 0
lim h→0+ [sin(0+h)]=sinh=0
lim h→0+ [h] =0
so for a no. slightly greater then 0 sinx=x.
so quetion is incorrect
