Show that the function f (x) := 1/x2 is uniformly continuous on (1, ∞), but that it isnot uniformly continuous on (0, ∞)

let f:X -> (0,inf) be a continuous function on a compact space X. show that there exits an ε >0 such that f(x)>=ε for all x element of X

9. Let f be the function from R to R defined by f (x) = x2. Finda) f −1({1}) b) f −1({x | 0 < x < 1}) c) f −1({x | x > 4})

Consider the function f : R → R defined by f (x)=1 if x∈ Q, f (x)=0 if x∈ R/Q, where is f continuous? be sure to prove your assertion

Let f (x) be a function that f ′(x) = x2 + 2x + 2. Suppose that f (−1) = −1. What is f (2)?A. -1B. 1C. 11D. 17E. -17

Determine whether the following functions are Riemann integrable on [0, 1] or not.(1) f (x) := sin √x√1 + x2