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Chapter 4 145 - 30 31 32 33 CHAPTER 4 REVIEW 407 y — f:c...

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Unformatted text preview: 30. 31. 32. 33. CHAPTER 4 REVIEW 407 y — f(:c) —4:c taunt. g< :r, <72r A. D — (—gg). B. y—intercept: f(()) : 0 C. f(—:r) = —f(:c) so the curve is symmetric about (0. 0). D. lim (4m — tan ac) : ~00. lim (4:1: — tan 3:) 2 00. so as = % w—nr/Z— I—V—1r/2'l” andm: —§ areVA. E. f’(:L') =4—sec2:c>0 41> secx<2 41> cosx >% c» —§ < :n < %. sof is increasing on (—g. g) and decreasingon (—g. ~§) and (gg). F. f(§) = 4?" ~ x/Bisa local maximum value. f(—§) 2 \/§ — 335 is a local minimum value. G. fH(:C) : —ZSec2xta11:c >0 <=> tana: < 0 <:> —% < a: < O. sof is CUon (790) and CD on (0. g). IP at (0,0) y : f($) : sin’1(1/:c) A. D 2 {av l —1 S 1/30 g 1}: (—00,—1]U[1.00). B. No intercept C. f(~a:) : —f(m) symmetric about the origin D. lim sin’1(1/a:) = sin’1 (0) : 0. so y = 0 is a HA. E. f’(;r) : W <—%> = fl < 0. so f is decreasing on (—00. —1) and (1. 00). F. No local extreme value, but f(1) : g is the absolute maximum value H. and f(—1) : ~§ is the absolute minimum value. 4333 _ 2x 25(2952 — 1) G.f (x):W:W>0for$>1and f”(m) < 0 for$ < 71. so f is CU on (1.00) and CD on (—00, —1). No IP y : f(a:) = rah—$2 A. D : R B. y-intercept 1; no x—intercept C. No symmetry D. lim 621‘22 : 0. z-—>:l:00 so y : 0 is a HA. E. y : f(:c) = 821‘“C2 :> f’(m) : 2(1— 9:)e2w_12 > 0 <:> a: < 1. so f is increasing 0n (~00. 1) and decreasing on (17 00). F. f(1) : e is a local and absolute maximum value. G. f"($):2(2a:274$+1)62r’m2:0 {i} m21:§. f”(ac)>0 (I) at<1—§or$>1+§.sofisCUon (—oo,1~ g) and (1+§700>.andCDon (1— flJ—l—fl). 1Pat(1i§.\/é) y : f(:c) : 8“” + 6‘3“ A. D : R B. y—intercept 2; no m—intercept C. No symmetry D. lim (61 + 6-3”) : 00. no asymptote E. y : f(:v) : ea” + 6-32 :> z—>::oo f/(ac) : ex 7 36‘33 : 6‘33” (64$ ~ 3) > 0 {I} 64$ > 3 <=> H. 4$ > ln3 (i) m > £1113 % 0.27. so f is increasing on 61113.00) and decreasing on (—00. i In 3), F. Absolute minimum value f6 1113) : 31/4 + 373/4 % 1.75. G. f”(:v) : ex + 98‘3“” > 0. so f is CU on (~00. 00). No IP ...
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