Prove or disapprove f(x) is uniformly continuous
f(x)=(sinx)/x for x not equal to zero.
and f(x)=1 for x=0
I know f(x) is uniformly continous but I can't prove it. how do i show the derivative $\displaystyle (xcosx-sinx)/x^{2}$ is bounded.
thanks
Prove or disapprove f(x) is uniformly continuous
f(x)=(sinx)/x for x not equal to zero.
and f(x)=1 for x=0
I know f(x) is uniformly continous but I can't prove it. how do i show the derivative $\displaystyle (xcosx-sinx)/x^{2}$ is bounded.
thanks
Take into account that the coefficients of McLaurin expansion of $\displaystyle x\cdot \cos x - \sin x$ of degree < 3 are equal to zero, so that is $\displaystyle f^{'}(0)=0$ and that both the functions $\displaystyle \frac{\cos x}{x}$ and $\displaystyle \frac{\sin x}{x^{2}}$ tend to 0 if x tends to infinity...
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$