CHEM 151B Midterm: CHEM 151B UCSC Exam1-2016
Document Summary
You have 60 minutes to answer all four questions. Consider a; b 2 r and prove the following: if 8" > 0; ja (cid:0) bj (cid:20) "; then a = b. Given a set x (cid:18) r, prove that if min x exists it is equal to inf x. Prove that the function de(cid:133)ned by d(x; y) = pn (with n (cid:21) 3). i=1 jxi (cid:0) yij with x; y 2 rn is a metric on rn. A metric is a function d : rn (cid:2) rn ! Let b be a closed subset of rn with the standard euclidean metric. Let a 2 rn such that a =2 b. De(cid:133)ne: f (a; b) = inffja (cid:0) bj : b 2 bg.
