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chapter 1 4 - 4 CHAPTER 1 FUNCTIONS AND MODELS 17(a N 2500...

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Unformatted text preview: 4 CHAPTER 1 FUNCTIONS AND MODELS 17. (a) N 2500 2000 1500 1000 500 0 1991 1 993 1995 1997 ’ 18. (a) 02468101214! midnight noon 19. f(:17)= 37:2 — a: + 2. f(2):3(2)2—2+2=12—2+2=12. f(—2) =3(—2)2 —(—2)+2: 12+2+2:16. f(a) :3a2 —a+2. f(#a) = 3(—a)2 — (—a) + 2 = 3612 + a + 2. (b) From the graph. we estimate the number of cell—phone subscribers in Malaysia to be about 540 in 1994 and 1450 in 1996. N 2500 2000 1500 1000 500 0 1991 1993 1995 1997 1 (b) From the graph in part (a), we estimate the temperature at 11:00 AM. to be about 845°C. f(a+1)=3(a+1)2—(a+1)+2:3(a2+2a+1)—a-—1+2=3a2+6a+3~a+1=3u2+5a+4. 2f(a):2‘f(a) 22(3a2—a+2):6a2#2a+4. f(2a) :3(2a)2 — (2a)+2=3(4a2) —2a+2= 12112 —2a+2. f(a2) = 3(a2)2 — (a2)+2:3(a4) —a2+2= 3114 —a2+2. 1mm? = [3.12 — a+ 212 = (3&2 — a + 2) (3.12 - a + 2) =9a4—3a3+6a2~—3a3+a2—2a+6a2—2a+4=9a4—6a3+13a2~4a+4. f(a+h)=3(a+h)2—(a+h)+2=3(a2+2ah+h2)—a#h+2=3a2+6ah+3h2—a#h+2. 20. A spherical balloon with radius r + 1 has volume V (7“ + 1): §n('r + 1)3 = %7T(T‘3 + 3T2 + 31" + 1). We Wish to find the amount of air needed to inflate the balloon from a radius of r to r + 1. Hence, we need to find the difference V(7" + 1) — V0") : §7r(r3 + 31'2 + 3’!" + 1) — §7rr3 2 $71137"2 + 37" + 1). 21. f(:c) : x~$2, so f(2+h):2+h—(2+h)2:2+h— (4+4h+h2)—21h 4 4h h2= (112131112), f(:c+h)=$+h—(x+h)2=x+h#(m2+2:ch+h2)=x+h—m2—2mh—h2,and f(a:+h)—f(a:) ‘m+h#$2—2wh—h2#:c+m2 h—2mh—h2 _ h(1—2m—h) h h :12 h. h h m ...
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