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chapter 2 79

# chapter 2 79 - CHAPTEBZ REVIEW E For a 2 0 m 2 6 and f(0 2...

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Unformatted text preview: CHAPTEBZ REVIEW E] For a 2 0. m 2 6 and f(0) 2 2. so an equation of the tangent line is y — 2 2 6(w — 0) or y 2 6x + 2. For a 2 —1. m 2 g and f(~1) 2 % so an equation ofthe tangent line is y — % 2 g a: + 1) org 2 3:2: + g. 39. (a) s 2 s(t) 2 1 + 2t + 152/4. The average velocity over the time interval [1. 1 + h] is _ 5(1+h)_3(1) _ 1+2(1+h)+ (1+h)2/4— 13/4 10h+h2 _10+h (1+ h) — 1 h 4h 4 So for the following intervals the average velocities are: (i) [1,3]: It 2 2. pave 2 (10 + 2)/4 2 3 m/s (ii) [1.2]: h 2 1.11aw 2 (10 +1)/4 2 2.75 m/s (iii) [1.15]: h 2 0.5. wave 2 (10 + 0.5)/4 2 2.625 m/s (iv) [1.1.1]: It 2 0.1. Dave 2 (10 + 0.1)/4 2 2.525 m/s Uavk‘ 1 — 1 1 h 10 (b) When t 2 1. the instantaneous velocity is lim w 2 lim 0 + 2 — 2 2.5 m/s. I120 h 1120 4 4 40. (a) When V increases from 200 in3 to 250 in3, we have AV 2 250 2 200 2 50 in3. and since P 2 800/V. AP 2 P(250) 2 P(200) 2 % — 3703 2 3.2 — 4 2 —0.81b/in2. So the average rate of change is AP —0.8 ib/in2 _ : — : 2 _ 16 . AV 50 0 0 in3 (b) Since V 2 800 / P, the instantaneous rate of change of V with respect to P is . AV ‘ . V(P+ h) — V(P) _ . 800/(P+ h) — SOO/P i133?) E _ i136 h ‘ til—rib h _ hm 800 [P 2 (P+h)] _ hm —800 _ [email protected] 320 h(P+h)P * h~>0 (P+h)P _ P2 which is inversely proportional to the square of P. . . — 2) . :103—2m—4 41. , : f(r) f( 2 W9) :13; .22 212% .H , (ac—2)(a:2+2x+2) 211m 222 15—2 : lim(m2+2m+2) =10 m—>2 (b)y—4210(m—2)0ry210m—16 42. 26 2 64, so f(;1:) 2 m6 and a 2 2. 43. (a) f’(r) is the rate at which the total cost changes with respect to the interest rate. Its units are dollars / (percent per year). (b) The total cost of paying off the loan is increasing by \$1200/( So if the interest rate goes up from 10% to 11%. the cost goes up approximately \$1200. (c) As r increases. C increases. So f’(r) will always be positive. percent per year) as the interest rate reaches 10%. 143 ...
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