Real Analysis Answers

The function f: R→R defined by f(x)= | x-1|+ | 3-x| is differentiable at x= 4.

True or false with full explanation

Find the local maximum and local minimum values of the function

f(x)= x^3-2x^2-4x+5

Examine the following series for convergence

∞Σn=1 [(n-1/(2n+3)]^n

Examine whether the equation, x^3-11x+9=0 has a real root in the interval, [-1,2]

Find whether the following series are convergent or not

ii. ∞Σn=1 (√(n^2+3) - √(n^2-3)/ √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

Show that the sequence (fn) sequence where

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