MAT 21A Study Guide - Midterm Guide: Jyj, Asymptote, Intermediate Value Theorem

• School: UC-Davis
• Department: Mathematics
• Course: MAT 21A
• Professor: All

Document Summary

1: [30%] evaluate the following limits or say if they do not exist. (a) lim x 2 (b) lim x 0 (c) lim x 0 (d) lim x 3 . 5x + 4 2 x sin(1/x) x x2 2x 3. |x 3: (a) since the limit of the denominator is non-zero, we have lim x 2. 11 23 = 3: (b) using the di erence of two squares to simplify the square root, we get. 5x + 4 2 x lim x 0 x 0(cid:0) 5x + 4 2(cid:1)(cid:0) 5x + 4 + 2(cid:1) x(cid:0) 5x + 4 + 2(cid:1) x(cid:0) 5x + 4 + 2(cid:1) 4: (c) this limit does not exist, since sin(1/x) oscillates in nitely often between 1 and 1 as x 0 and the limit of the denominator x is 0. 2: (d) if x < 3, then |x 3| = 3 x, so lim x 3 x2 2x 3.