Recent content by riskandar

Homework Statement f(x) = (3 sin(x))/(2 + cos(x)) let x_0 be a number in (0, (2/3)*pi], and define a sequence recursively by setting x_n+1 = f(x_n) (1) prove that the sequence {x_n} is strictly decreasing sequence in (0, (2/3)*pi] and that lim x_n =0 (2) Find an integer k greater or equal...

Thank you for the reply. Where do I use the intermediate value theorem? Is it to prove surjective?

Homework Statement let f: R->R be a continuous function Suppose k>=1 is an integer such that lim f(x)/x^k = lim f(x)/x^k = 0 x->inf x->-inf set g(x)= x^k + f(x) g: R->R Prove that (i) if k is odd, then g is surjective (ii) if k is even, then there is...