Real Analysis Answers

Show that the sequence (fn) sequence where

fn(x)= x/(1+nx^2), x∈[2,∞] is uniformly convergent in [2,∞]

Let f(x)=x, show that f is Riemann integrable in the interval [a,b]. Hence find the Riemann integral of f.

Prove that the sequence {an/n} is convergent where { an} is a bounded sequence

test the series : infinity sigma n=1 (-1) ^n-1 sin nx/n√n for absolute and conditional convergence

Prove that continuous function of a continuous function is continuous.

Using the principle of induction, prove that 64 is a factor of 3^(2n+2)- 8n-9 ∀ n∈N

Sketch the graph of the function, f defined by

f(x)= |x-3| +[x], x∈ [2,4] where [x] denotes the greatest integer function