Question

Section 2.6 Homework (continued) D. Determine the end behavior of the following function. (Do this algebraically.) $ 16x8 – 12x2 f(x) = 1- 7x² + 5x 70 + 2X-8 C. Find the limit or show that it does not exist. (a.) lim n sin²x " (Hint: Use squeeze theorem) X x²+1 (b.) lim cot?(-Inx) (Do this analytically.) X-> Section 2.6 Homework (continued) E. Find the following limits if they exist. Explain. (Do this analytically (a.) lim cot' (In 10 - 8x) (b.) lim cos arccsc Section 2.6 Homework (continued) F. Determine the equation(s) of any vertical asymptotes of the following functions. Use the following definition of a vertical asymptote as your justification the line r = a is DEFINITION Vertical Asymptote If lim f(x) = t , lim f(x) = 50. or lim f(x) = t called a vertical asymptote off. (a.) y = In (x-1) (b.) y = cot (2x) on (0,2x)

Answer 1

(b) lim Cott (- lon) 00 lim n o Cot(lon) limo Calt (lnxt) limo Cat" (An 1/n) by the log Property alobalna we can wright Ihon = lore - kniha so lim o Cat" (len/n) - cott (An Yoe) - Cot" (aln(o)) = Cot" (lo(o) we know that to (o) = -00 hence M >00 lim Coth (en (0)) =- Cot" (oo) --Cot' (Cot(o)) lim Cat" (-la (41) = 0 Ang