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chapter 2 1

chapter 2 1 - 2 El LIMITS AND DERIVATIVES 2.1 The Tangent...

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Unformatted text preview: 2 El LIMITS AND DERIVATIVES 2.1 The Tangent and Velocity Problems 1. (a) Using P(15. 250). we construct the following table: (c) From the graph. we can estimate the slope of the tangent line at P to be it Q slope = me # = *333' 5 (5.694) 6954:5550 = ~% : —44.4 444—250 1 194 _ g 700 - 10 (10-1444) — T - 388 :33 ”3333333.... 111—250 _ g 1 _ 0 - . 20 (20., 111) m 1 ~ 5 — 27.8 72 :30 aggrﬂrlnsée 25 (25, 28) ——2285-_21550 : —% = ‘22 g > 30 (30.0) 36.213 : —% : —16.6 (b) Using the values of t that correspond to the points closest toP(t: 10 andt: 20), we have r( m ) — . —2 .8 m 2 _33.3 2 2. (a) Slope : W : % as 69.67 (b) Slope : W : ¥ : 71.75 (c) Slope = 529333306 2 ¥ 2 71 (d) Slope = “3033:3348 = % = 66 From the data, we see that the patient’s heart rate is decreasing from 71 to 66 heartbeats / minute after 42 minutes. After being stable for a while. the patient’s heart rate is dropping. 3. For the curve y : 33/(1 + it) and the point P(1. 2) (a) (b) The slope appears to be i. a: Q mPQ . —r— —' (1) 0.5 (05. 0.333333) 0.333333 1 1 .. (C)y*§:z(x71)or (11) 0.9 (0.9, 0.473684) 0.263158 1 1 = — + 7 (111) 0.99 (0.99. 0.497487) 0.251256 9 49C 4 (iv) 0.999 (0.999, 0.499750) 0.250125 (v) 1.5 (1.5, 0.6) 0.2 (v1) 1.1 (1.1, 0.523810) 0.238095 (vii) 1.01 (1.017 0.502488) 0.248756 (viii) 1001—J (1.0017 0.500250) 0.249875 J 65 ...
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