MATH 1161.01 Study Guide - Midterm Guide: Product Rule, Quotient Rule, Asymptote

• School: Ohio State University
• Department: Mathematics
• Course: MATH 1161.01
• Professor: All

Document Summary

Problem 1. (asymptotes via limits): (1) determine the vertical asymptotes of f (x) = Solution. (1) note that the numerator and denominator factor as follows: 24x3 6x2 + 8x 2 = 6x2(4x 1) + 2(4x 1) Thus the numerator and denominator share a common factor of 4x 1, and the reduced form of f (x), and the reduced form of f (x) is the function g(x) = 2(3x2 + 1) x 2 (this also shows that f (x) has a removable discontinuity at x = 1/4. ) Note f (x) is well-de ned for all x 6= 1/4, 2, since the numerator and denominator of f are nonzero. Also 2(3x2 + 1) is bounded in an interval around x = 2, so that x 2 0 as x 2 implies (cid:12)(cid:12)(cid:12) vertical asymptote at x = 2. 2(3x2+1) x 2 (cid:12)(cid:12)(cid:12) as x 2.