prove that $\displaystyle f(x)=sin(lnx)$continues uniformly in $\displaystyle [1,\infty)$
prove that for all $\displaystyle \delta>0 $exists natural 'n' so $\displaystyle e^{\frac{\pi}{2}-2\pi n}-e^{-2\pi n}<\delta$
prove that $\displaystyle f(x)=sin(lnx)$ is not uniformly continues in (0,1)
in part d we can use part c

regarding part A:
i want to show that the derivative of f(x) is bounded then its automatickly uniformly continues.
$\displaystyle f'(x)=\frac{cos(lnx)}{x}\leq \frac{1}{x} $
so when we got to infinity the 1/x goes to zero.but if we got to x=0 the 1/x goes to infinity
why it is bounded