Show that a continuous function f : [0, 1] → Z is a constant function.

Q: Suppose that g is a continuous function. Find the general solution of y" – y = g(t).

A:

Q: Let X be Hausdorff and f : X → X be a continuous function. Show that {x : f (x) = x} is closed in X.

A: Let, .We show  is open and so F is closed.

Q: Let f(x) = V5x² – 20. Find everywhere f is continuous. -

A: Given fx=5x2-20

Q: b) Give an example of a function g: R →R that is continuous at some xE R, but not differentiable at…

A:

Q: Show that the function f: C → C given by f(z) = z2 is continuous on C.

A:

Q: "Prove that the function f : R→ R with ƒ(x) = = is uniformly continuous."

A:

Q: Let f(x) = |x|+|x−2], x € R. Find points where f is not differentiable.

A:

Q: Let h : R → R be some twice-differentiable function. Define f(x,y) = h(x) for all x ≠ 0. Show that…

A:

Q: q17. Let f, g, h be continuous functions on an interval [a, b]. If f is orthogonal to g and to h,…

A:

Q: Suppose that the function f: [0, 1] in R is continuous and thatf(x) > 2      if 0<=X < 1.Is…

A:

Q: Rewrite the following integral using the indicated order of integration and then evaluate the…

A:

Q: Define the function zlm(z) z +0 f(2) = Z = 0 1. Prove that f is continuous at the origin. 2. Prove…

A: This question is related to complex analysis . Topic is continuity and differentiability.