Which of following is not a valid expression? (i) 7.5 (ii) b + a = c (iii) {feet:10, inches:5} (iv) [2,3,6,9,5,7]
Answers
Answers to Selected Exercises
Chapter 0
Section 0.1
1. −48 3. 2/3 5. −1 7. 9 9. 1 11. 33 13. 14
15. 5/18 17. 13.31 19. 6 21. 43/16 23. 0
25. 3*(2-5) 27. 3/(2-5) 29. (3-1)/(8+6)
31. 3-(4+7)/8 33. 2/(3+x)-x*y^2
35. 3.1x^3-4x^(-2)-60/(x^2-1) 37. (2/3)/5
39. 3^(4-5)*6 41. 3*(1+4/100)^(-3)
43. 3^(2*x-1)+4^x-1 45. 2^(2x^2-x+1)
47. 4*e^(-2*x)/(2-3e^(-2*x)) or 4*(e^(-2*x))/
(2-3e^(-2*x)) 49. 3(1-(-1/2)^2)^2+1
Section 0.2
1. 27 3. −36 5. 4/9 7. −1/8 9. 16 11. 2 13. 32
15. 2 17. x5 19. − y
x 21.
1
x 23. x3 y 25. z4
y3 27. x6
y6
29. x4 y6
z4 31.
3
x4 33.
3
4x2/3 35. 1 − 0.3x2 − 6
5x 37. 2
39. 1/2 41. 4/3 43. 2/5 45. 7 47. 5 49. −2.668
51. 3/2 53. 2 55. 2 57. ab 59. x + 9 61. x
√3 a3 + b3
63.
2y
√x 65. 31/2 67. x3/2 69. (xy2)1/3 71. x3/2
73.
3
5
x−2 75.
3
2
x−1.2 − 1
3
x−2.1 77.
2
3
x − 1
2
x0.1 +
4
3
x−1.1
79. (x2 + 1)−3 − 3
4
(x2 + 1)−1/3 81. √3 22 83. √3 x4
85. 5
√x √3 y 87. − 3
2
√4 x 89.
0.2
√3 x2 +
3
√x
7
91.
3
4
-
(1 − x)5 93. 64 95. √3 97. 1/x 99. xy
101. y
x
1/3
103. ±4 105. ±2/3 107. −1, −1/3
109. −2 111. 16 113. ±1 115. 33/8
Section 0.3
1. 4x2 + 6x 3. 2xy − y2 5. x2 − 2x − 3
7. 2y2 + 13y + 15 9. 4x2 − 12x + 9 11. x2 + 2 + 1/x2
13. 4x2 − 9 15. y2 − 1/y2 17. 2x3 + 6x2 + 2x − 4
19. x4 − 4x3 + 6x2 − 4x + 1 21. y5 + 4y4 + 4y3 − y
23. (x + 1)(2x + 5) 25. (x2 + 1)5(x + 3)3(x2 + x + 4)
27. −x3(x3 + 1)√x + 1 29. (x + 2)-
(x + 1)3
31. a. x(2 + 3x) b. x = 0, −2/3 33. a. 2x2(3x − 1)
b. x = 0, 1/3 35. a. (x − 1)(x − 7) b. x = 1, 7
37. a. (x − 3)(x + 4) b. x = 3, −4 39. a. (2x + 1)(x − 2)
b. x = −1/2, 2 41. a. (2x + 3)(3x + 2)
b. x = −3/2, −2/3 43. a. (3x − 2)(4x + 3)
b. x = 2/3, −3/4 45. a. (x + 2y)2 b. x = −2y
47. a. (x2 − 1)(x2 − 4) b. x = ±1, ±2
Section 0.4
1.
2x2 − 7x − 4
x2 − 1
3.
3x2 − 2x + 5
x2 − 1
5. x2 − x + 1
x + 1
7. x2 − 1
x 9.
2x − 3
x2 y
11. (x + 1)2
(x + 2)4 13. −1
-
(x2 + 1)3
15. −(2x + y)
x2(x + y)2
Section 0.5
1. −1 3. 5 5. 13/4 7. 43/7 9. −1 11. (c − b)/a
13. x = −4, 1/2 15. No solutions 17. ±
5
2
19. −1
21. −1, 3 23.
1 ± √5
2
25. 1 27. ±1, ±3
29. ±
−1 ± √5
2
31. −1, −2, −3 33. −3 35. 1
37. −2 39. 1, ±
√5 41. ±1, ±
1
√2
43. −2, −1, 2, 3
Section 0.6
1. 0, 3 3. ±
√2 5. −1, −5/2 7. −3 9. 0, −1, 1
11. x = −1 (x = −2 is not a solution.) 13. −2, −3/2, −1
15. −1 17. ±√4 2 19. ±1 21. ±3 23. 2/3 25. −4, −1/4
Chapter 1
Section 1.1
1. a. 2 b. 0.5 3. a. −1.5 b. 8 c. −8 5. a. −7 b. −3
c. 1 d. 4y − 3 e. 4(a + b) − 3 7. a. 3 b. 6 c. 2 d. 6
e. a2 + 2a + 3 f. (x + h)2 + 2(x + h) + 3 9. a. 2
b. 0 c. 65/4 d. x2 + 1/x e. (s + h)2 + 1/(s + h)
f. (s + h)2 + 1/(s + h) − (s2 + 1/s) 11. a. 1 b. 1 c. 0
d. 27 13. a. Yes; f (4) = 63/16 b. Not defined
c. Not defined 15. a. Not defined b. Not defined
c. Yes, f (−10) = 0 17. a. h(2x + h) b. 2x + h
19. a. −h(2x + h) b. −(2x + h)
21. 0.1*x^2-4*x+5
23. (x^2-1)/(x^2+1)
25. a. P(5) = 117, P(10) = 132, and P(9.5) ≈ 131. Approxi-
mately 117 million people were employed in the U.S. on July 1,
1995, 132 million people on July 1, 2000, and 131 million peoplr.
In the above mentioned expressions (i) 7.5 is not a valid expression
EXPLANATION:
An expression is a combination of operators and operands that can be evaluated. It may also include function calls which return values.
(i) 7.5 is not any kind of expression. Only a number
(ii) b + a = c // b is variable in this expression
(iii) {feet:10, inches:5} // is an object literal
(iv) [2,3,6,9,5,7] // this is an array literal