You could instead try to show that the derivative is bounded. If this is the case, then by the Mean Value theorem, . Choosing gives , and we have uniform convergence.
Try to show that is bounded.
Prove is uniformly continuous over R
Stuck on this one
So I'm trying to show for appropiate , and , that
So
Known that
Using triangle inequality and considering the numerator only
And here I'm stuck.
Hints please and thank you