1) Limit as x-->1- (from the right) of: sqrt(1-x^2) / sqrt(1-x^3)
(I know that I need to apply L'Hopital's rule here, maybe even twice, but I keep getting the wrong answer. Thanks in advance if you can help!)
2) Let f be a twice differentiable function and fix a value of x.
(a) Show that
lim as h-->0: [f(x+h)-f(x-h)]/2h = f '(x)
(b) Show that
lim as h-->0: [f(x+h)-2f(x)+f(x-h)]/(h^2) = f ''(x)