MTH 151 Study Guide - Quiz Guide: 2 On
Document Summary
Sep 11, 2007: ketchersid, [9pts] a) [3pts] give the rigorous ( - ) de nition of limx 3. For all > 0, there is a > 0 such that. 1 (cid:12)(cid:12)(cid:12)(cid:12) (cid:12)(cid:12)(cid:12)(cid:12) < : [3pts] find an interval (xl, xr) (for arbitrary ) satisfying xl < x < xr 1 < 1 (see graph. ) For xl you must solve xl 2 = 1 + so xl 2 = 1. Similarly compute xr. x 2 < 1 + . 1 : [3pts] use the above to give a satisfying 0 < |x 3| < (cid:12)(cid:12)(cid:12) 1 x 2 1 (cid:26) (cid:27) = min{3 xl, xr 3} = min. 1 + (cid:12)(cid:12)(cid:12) < . (cid:27) (cid:26) Use your to nd: (give actual numbers with at least 4 decimal places of accuracy. ) There is some x0 so that for x x0, |f(x)| < 1/2 since limx f(x) = 0. By extreme value theorem f(x) has a maximum value m on [0, x0].
