Calculus And Its Application 12th Edition By Larry J. Goldstein, David I. Schneider, David C. Lay, Nakhle H. Asmar (Solutions Manual, All Chapters 100% Original Verified, A+ Grade) Chapter 0 Functions 0.1 Functions and Their Graphs 1. 2. 3. 4. 5. 6. 7.[2, 3) 8. 31,2⎛⎞−⎜⎟⎝⎠
9.[–1, 0) 10. [–1, 8)
11.(),3−∞ 12.) 2,⎡∞⎣
13.2() 3fx x x=−
2(0) 0 3(0) 0f=− =
2(5) 5 3(5) 25 15 10f=− =−=
2(3) 3 3(3) 9 9 0f=− = − =
2( 7) ( 7) 3( 7) 49 21 70f−= − −−= + =
14.2() 9 6fx x x=− +
2(0) 9 6(0) 0 9 0 0 9f=− + =−+=
2(2) 9 6(2) 2 9 12 4 1f=− + =− +=
2(3) 9 6(3) 3 9 18 9 0f=− + =− +=
2(1 3 ) 9 6 (1 3 ) (1 3 )
9 78 169 256f−= − −+ −
=+ + =
15.32() 1 fx x x x=+− −
32(1) 1 1 1 1 0f=+− − =
32(1 ) (1 ) (1 ) (1 ) 1 0f−= − + − − −−=
3211 1 1 9122 2 2 8f⎛⎞ ⎛⎞ ⎛⎞ ⎛⎞=+− − = −⎜⎟ ⎜⎟ ⎜⎟ ⎜⎟⎝⎠ ⎝⎠ ⎝⎠ ⎝⎠
32() 1 fa a a a=+− −16.32() 3gt t t t=− +
32(2) 2 3(2) 2 8 12 2 2g=− + = −+ = −
3211 1 1322 2 2
131 1 1
842 8g⎛⎞⎛ ⎞ ⎛ ⎞ ⎛ ⎞−= − −− + −⎜⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝⎠⎝ ⎠ ⎝ ⎠ ⎝ ⎠
=− − − =−
3222 2 2333 3 3
81 2 2 1 0.370372 793 2 7⎛⎞ ⎛⎞ ⎛⎞ ⎛⎞=− +⎜⎟ ⎜⎟ ⎜⎟ ⎜⎟⎝⎠ ⎝⎠ ⎝⎠ ⎝⎠
=−+ = −≈ −g
32() 3ga a a a=− +
17. ()(1 )shss=+
()11
22
3 1
2 211
23 1h⎛⎞== =⎜⎟⎝⎠+
()33
22
1 3
2 2332 1h−− ⎛⎞−= = =⎜⎟⎝⎠ −+−
11(1 )1( 1 ) 2aahaaa+++= =++ +
18. 2
2()
1xfx
x=
−
()
()21 1
2 4
2114211
23 11f⎛⎞== = −⎜⎟⎝⎠ −−
()
()21 1
2 4
2114211
23 11f−⎛⎞−= = = −⎜⎟⎝⎠ −−−
22
22
2
2(1 ) 21(1 )
(1 )1 ( 21 ) 1
21
2aa afa
aa a
aa
aa++ ++= =
+− ++ −
++=
+
19.2() 2fx x x=−
2
22( 1) ( 1) 2( 1)
(2 1 ) 2 2 1fa a a
aa a a+=+ − +
=+ + − − = −
2
22( 2) ( 2) 2( 2)
(4 4 ) 2 4 2fa a a
aa a aa+=+ − +
=+ + − − = +
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. 2 Chapter 0: Functions 20. 2() 4 3fx x x=++ 2
2
2(1 ) (1 )4 (1 ) 3
(2 1 ) ( 4 4 ) 3
2fa a a
aa a
aa−=− + −+
=− + +− +
=+ 2
2
2( 2) ( 2) 4( 2) 3
(4 4 ) ( 4 8 ) 3
1fa a a
aa a
a−=− + −+
=− + +− +
=− 21. a. f(0) represents the number of fax machines sold in 1990. b. 2 1(2) 50 4(2) (2)2
50 8 2 60f=+ +
=+ + = 22. 100() ,=+xRxbx x ≥ 0 a. b = 20, x = 60 100(60)(60) 7520 60R==+ The solution produces a 75% response. b. If R(50) = 60, then 100(50)6050
60 3000 5000
100
3b
b
b=+
+=
= This particular frog has a positive constant of 33.3. 23. 8()(1 ) (2 )xfxxx=−− all real numbers such that x ≠ 1, 2 or ()()() ,1 1 , 2 2 ,−∞ − ∪ − ∪ ∞ 24. 1()ft
t= all real numbers such that t > 0 or ()0,∞ 25. 1()
3gx
x=
− all real numbers such that x < 3 or (),3−∞ − 26. 4()(2 )gxxx=+ all real numbers such that x ≠ 0, –2 or ()()() ,2 2 , 0 0 ,−∞ − ∪ − ∪ ∞ 27. function 28. not a function 29. not a function 30. not a function 31. not a function 32. function 33. 1 34. –1 35. 3 36. 0 37. positive 38. negative 39. positive 40. yes 41. –1, 5, 9 42. [][] 1, 5 , 9,−∞ 43. .03 44. .03 45. .04 46. 3 47. ()1() 22fx x x⎛⎞=− +⎜⎟⎝⎠ 12 5(3) 3 (3 2)22f⎛⎞=− +=⎜⎟⎝⎠ Thus, (3, 12) is not on the graph. 48. f(x) = x(5 + x)(4 – x) f(–2) = –2(5 + (–2))(4 – (–2)) = –36 So (–2, 12) is not on the graph. 49. 231()
1xgx
x−=
+ ()
()1 1
2 2
2514231 12
351g−⎛⎞== =⎜⎟⎝⎠+ So 12,25⎛⎞⎜⎟⎝⎠ is on the graph. 50. 2(4 )()(2 )xgxx+=+ ()22 40
3 9
28
3 34 25
33 2g+⎛⎞== =⎜⎟⎝⎠+ So 25,33⎛⎞⎜⎟⎝⎠ is on the graph. 51. 3()fx x= 3(1 ) (1 )fa a+=+ 52. 5()fx xx⎛⎞=−⎜⎟⎝⎠ 225(2 ) (2 )(2 )
5( 2 ) 14
(2 ) 2fh hh
hh h
hh+= −++
−+ −−==++ Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Section 0.1: Functions and Their Graphs 3 53. for 0 2()
1f o r 2 5xxfx
xx⎧ ≤< ⎪=⎨+≤ ≤⎪⎩ (1) 1 1f== f(2) = 1 + 2 = 3 f(3) = 1 + 3 = 4 54. 21for 1 2
()
for 2xx fx
xx⎧≤≤ ⎪=⎨
⎪< ⎩ 1(1) 11f== ; 1(2)2f= 2(3) 3 9f== 55. 2for 2
() 1 f o r 2 2 . 5
4 for 2.5xx
fx x x
xxπ⎧ <
⎪=+ ≤≤⎨
⎪<⎩ 2(1) (1)fππ== f(2) = 1 + 2 = 3 f(3) = 4(3) = 12 56. 23for 24
() 2 f o r 2 3
5f o r 3xx
fx x x
xx⎧<⎪−⎪=≤ <⎨
⎪
−≤⎪⎩ 3(1) 141f==− f(2) = 2(2) = 4 2(3) 3 5 4 2f=− = = 57. .06 for 50 300
( ) .02 12 for 300 600
.015 15 for 600xx
fx x x
xx≤≤ ⎧
⎪=+ < ≤⎨
⎪+>⎩ 58. 59. 60. Entering Y1 = 1/X + 1 will graph the function 1() 1fxx=+ . In order to graph the function 1()1fxx=+, you need to include parentheses in the denominator: Y1 = 1/(X + 1) . 61. Entering Y1 = X ^ will graph the function ()4xfx3
= . In order to graph the function 34yx= , you need to include parentheses in the exponent: Y1 = X ^ (3/4) . 62. Y1 = X^3 − 33X^2 +120X+1500 [−8, 30] by [−2000, 2000] 63. Y1 = −X^2+2x+2 [−2, 4] by [−8, 5] 64. Y1 = (X+1)^(1/2) [0, 10] by [−1, 4] 65. Y1 = 1/(X^2+1) [−4, 4] by [−.5, 1.5] Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
