Math 226, HW5, due on Friday, October 20 1. Section 12.6: 1, 4, 17, 19 2. Chapter 12, Review Exercises: 4,5 3. Let a1 , . . . , am be real numbers. Show that v uX m u m 2 X |ai | t aj |ai | j=1 i=1 (the first inequality holds for all i). 4. Recall that for x, y Rn v u n uX |x y| := t (xi yi )2 i=1 Write f : Rn Rm as f (x1 , . . . , xn ) = (f1 (x1 , . . . , xn ), . . . , fm (x1 , . . . , xn )). Let L = (L1 , . . . , Lm ) Rm . Precise \u000f definition of limxx0 f (x) = L: \u000f > 0 > 0 such that if 0 < |x x0 | < , then |f (x) L| < \u000f. Show that lim f (x) = L iff for each i = 1, . . . , m, lim fi (x) = Li xx0 xx0 1