Real Analysis Answers

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

<e> Examine the f:R->R defined by

f(x)={1/6(x+1)^3 x is not equal to 0

5/6 x=0}

for continuity on R .If it is not continuous at any of R find the nature of discontinuity there

The function f(x)= [x]- x is not integrable in [ 0,3] , where [ x] denote greatest integer function.

True or false with full explanation

Does the sequence 3+ (-1)^n converge to 2. Justify

Does the sequence 3+ (-1)^n converge to 2. Justify

Show that the function f defined by f(x)= 1/x^2 is uniformly continuous on [a, ∞] , a> 0