Question

show 1/(x^1/2) is not uniformly continuous on the interval (0,1).

Answer #1

Prove that the function f(x) = x2 is uniformly
continuous on the interval (0,1).

Show that the function f(x) = x^2 + 2 is uniformly continuous on
the interval [-1, 3].

prove that these functions are uniformly continuous on
(0,1):
1. f(x)=sinx/x
2. f(x)=x^2logx

prove that this function is uniformly continuous on
(0,1):
f(x) = (x^3 - 1) / (x - 1)

Let f: (0,1) -> R be uniformly continuous and let Xn be in
(0,1) be such that Xn-> 1 as n -> infinity. Prove that the
sequence f(Xn) converges

Show that if f and g are uniformly continuous on some interval I
then cf (for all c ∈ R) and f − g are all uniformly continuous on
I

1.) Given the continuous function ?-4x in the
interval [0,1], determine the Fourier coefficients
??,?1,?2,?3.
2.) Reconstruct an approximation to ?-4x by using the
four coefficients found in part 1 (above). Plot the resulting
function in the interval [0,1].

Show that f: R -> R, f(x) = x^2 + 2x is not uniformly
continuous on R.

Let f: [0,1] -> [0,1] be a continuous function. Show that
there exists xsubzero [0,1] such that f(xsubzero)=xsubzero

Let X be a continuous random variable uniformly distributed on
the interval (0,2). Find E( |X-μ| )
A. 1/12 B. 1/4 C. 1/3 D. 1/2

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