Real Analysis Answers

Check whether the function, ,f defined below, is uniformly continuous or not:

f(x)=x^(1/2), x∈[1,2]

Prove or disprove the following statement

‘ Every strictly increasing onto function is invertible'

Is every onto strictly decreasing function invertible? Justify your answer.

All strictly monotonically decreasing sequences are convergent.

True or false with full explanation

For all even integral value of n, lim (x+1)^-n

n to ∞

Exist or not

True or false with full explanation

Test whether the series ∞Σn=0 1/(n^5+x^3) converges uniformly or not

A real function f defined on an interval [a,b] with a<c<b where c is a point of the interval, is said to be differentiable at the point x=c if

Applying Cauchy’s mean value theorem to the function f and g defined as f(x)=x2 and g(x)=x for all x∈[a,b], gives

Test whether the series ∞Σn=0 1/(n^5+x^3) converges uniformly or not