Ex 2_4 - 94 Chapter : L imits nd C ontinuity 2 a TXAMPLE 4...

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94 Chapter 2: Limits and Continuity FIGURE 2.41 The iuncrion in Exanple i4has an oblique asybptotc. EXERCISES 2.4 g. lim- /(r) = I i. Iib /(r) = 0 k. lin f(') does nol exisl. Which of tle tbllo$lng statemenrs aboul the function | : l(r) Craphed here de true. and which are falsc? TXAMPLE 14 Find the oblique asymprote for lhe graph of J\r): soLltion By long division, uc find ]:t+4 /2 s\ 15 \/ 49/ 4o(7l + 4) ;;;; -;t*. As -r + ao., the remainder, whose magnitude gives the \,erlicat distance between l}x graphs of/ andg, goes to zcro, naking the (slanted) li.e ,, 2 8 8''r,_ ^' 19 an as'rnptote ofthe gmph of/ (Figure 2.4t). Thc line _f = a(j) is an asymptote borh ..: the righl and to th€ ]eft. In the nexr section you will se€ thar the funciion l(r) gros. arbitarily large in absolute value as j approaches 4/7, whcre the denominator bccom.: zero (Figure 2.41). l. Which ol lhe following sratements aboul lhe tuction I : /Lrl gra|hed here are true. ed ehich are false? I lrn- l0) dcs nol *rt lim /(rl = 2 lr'l /G) does no1q6r. k. lim l(r) does not cxist. c. lim /(r) : 2 li. . l(r) = 0 t g. lin /(r): lim /frl ]". "' *''".'.'.' In rhe, ocn In,e^dr, r. I lin /G) disls at wcry. h the open inrerval0,l). d. lrm lh) = lim /(rl i lim /(r) = 2 l. liq lG) = 0 = {i. ,: 2, Find lim.,, lG) md tihj-r /(r). Does lin -: l(-r) exist:)Ifso, *hal is it? Ifrot. xbr not.l Fiid Iin
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0ne-Sjded Ljmits and Limits at lrfiijty .. Find 1im!,2 l(r),lln. ., /(-r, aid /(2).
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This note was uploaded on 05/08/2011 for the course ACCOUNTING 121210 taught by Professor Sdasdas during the Spring '10 term at Albany College of Pharmacy and Health Sciences.

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Ex 2_4 - 94 Chapter : L imits nd C ontinuity 2 a TXAMPLE 4...

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