Suppose that function f:[0,2]->R is continuous at [0,2], differentiable at (0,2) and such that f(0)=0, f(1)=1 and f(2)=1. a) Show that there is a x1 that belongs to (0,1) such that f'(x1)=1. b) Show that there is a x2 that belongs to (1,2) such that f'(x2)=0. c) Sho...
Calculate the limit: lim(((arccos x)^(n+1))/((arccos x)^n) with x tends to 1-, for every n that belongs to N, and then prove that lim(((arccos x)^n)/(arccos x))=sprt(n).