4)b)
prove that f(x)=sin(lnx)continues uniformly in [1,\infty)
4)c)
prove that for all \delta>0 exists natural 'n' so e^{\frac{\pi}{2}-2\pi n}-e^{-2\pi n}<\delta
4)d)
prove that 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.
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
?