Problem 2 (1 marks). Prove the following proposition. Proposition 1 Let U C R be open....

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Problem 2 (1 marks). Prove the following proposition. Proposition 1 Let U C R" be open. If f: U → R is differentiable at x E U, there are positive real numbers ŋ and K such that ||u – x|| < n implies If (u) – f(x)| < K ||u – x||. Hint: Try using the e, & definition with e = 1. And recall that for any two real numbers a, b, one has lal-1비 < la-b. Problem 2 (1 marks). Prove the following proposition. Proposition 1 Let U C R" be open. If f: U → R is differentiable at x E U, there are positive real numbers ŋ and K such that ||u – x|| < n implies If (u) – f(x)| < K ||u – x||. Hint: Try using the e, & definition with e = 1. And recall that for any two real numbers a, b, one has lal-1비 < la-b.