MATH114 Lecture Notes - Lecture 12: Indeterminate Form
2 Oct 2018
School
Department
Course
Professor
MATH114 verified notes
12/19View all
Document Summary
To determine the limits of rational functions as they approach , factor the numerator and the denominator by the largest power of x in function. The largest power of x in the function is(cid:2870), thus you have to factor it out from both the numerator and denominator: Then as (cid:2870)is common in both the numerator and denominator, they cancel out to give: lim (cid:2870)(cid:4666)(cid:886) (cid:883)(cid:882)+9(cid:882)(cid:882)(cid:2870)(cid:4667) (cid:2870)(cid:4666)(cid:885)+(cid:883) (cid:883)(cid:2870)(cid:4667) lim (cid:4666)(cid:886) (cid:883)(cid:882)+9(cid:882)(cid:882)(cid:2870)(cid:4667) (cid:4666)(cid:885)+(cid:883) (cid:883)(cid:2870)(cid:4667) lim (cid:3118)(cid:4666)(cid:2872) (cid:3117)(cid:3116)+9(cid:3116)(cid:3116)(cid:3118)(cid:4667) (cid:3118)(cid:4666)(cid:2871)+(cid:3117) (cid:3117)(cid:3118)(cid:4667) = 4/3. From the limit laws, each term in the numerator and denominator can be evaluated by the limit independently. Thus: factor out highest power of x, cancel the common factor lim (cid:2870)(cid:4666)(cid:883)(cid:889) +9(cid:882)(cid:882)(cid:2870)(cid:4667) (cid:2870)(cid:4666)(cid:883) (cid:883)(cid:882)(cid:882)(cid:2870)(cid:4667) lim (cid:4666)(cid:883)(cid:889) +9(cid:882)(cid:882)(cid:2870)(cid:4667) (cid:4666)(cid:883) (cid:883)(cid:882)(cid:882)(cid:2870)(cid:4667, evaluate each term by the limit lim (cid:4672)(cid:2869)7 +9(cid:3116)(cid:3116)(cid:3118)(cid:4673) (cid:4672)(cid:2869) (cid:3117)(cid:3116)(cid:3116)(cid:3118)(cid:4673) =(cid:2868)(cid:2869)=(cid:882) Vertical and horizontal asymptotes occur when the limit of a function dne therefore approaches positive or negative infinity.
