MATH117 Study Guide - Midterm Guide: Limit Of A Sequence, Limit Point, Scilab
Document Summary
You are allowed to refer to results that have appeared in class or in homework as long as you cite the result (except when the entire problem was done in class or in homework). Use one examination booklet as scratch paper, and submit the other one. Write the following de nitions: (a) a convergent sequence (b) the completeness axiom. Prove that if f is di erentiable at a then f is continuous at a. State and prove the maximal principle. (cid:16) cos5(cid:0) x2 x 1 (cid:1)(cid:17)0. 2x2 3x + cos x x3 + 1 x cos 1 x. True or false: sup(xn+yn) = sup xn+sup yn for any two sequences (xn) and (yn). Let xn = sin n. prove that (xn) has an accumulation point. Prove that if x a f (x) = + then lim x a lim.
