# Question: Prove that if f Rn Rm is differentiable

Prove that if f: Rn → Rm is differentiable at a € Rn, then it is continuous at a.

**View Solution:**## Answer to relevant Questions

A function f: R2 → R is said to be independent of the second variable if for each x € R we have f (x, y1) = f (x, y2) for all y1, y2. €R Show that f is independent of the second variable if and only if there is a ...Let f: Rn →R be a function such that | f (x) | ≤ |x|2 . Show that f is differentiable at 0Le Ei, i = 1,., k be Euclidean spaces of various dimensions. A function f: E1 X. X Ek→Rp is called multi linear if for each choice of xj € Ej, j ≠ I the function f: Ei→Rp defined by g(x) = f(x1,.,xi-1, ...Let A= {x, y}: x a. Let f : R → R be defined by F (x) = {x 2 sin 1/x) x ≠ 0, 0 x = 0.Post your question