Calculus- Early Transcendentals, 2021a

Selected Exercise Answers
1.1.1 1.
2.
3.
√ xy
2
3√ x
x
y
4. y = 3/2, y-intercept: 3/2, no x-intercept
5. y =(−2/3)x − 2, −2, −3
1.2.3 Yes, the lines are parallel as they have the same slope of
−1/2
1.1.2 a = 2, b = − 5 3 , c = 3 2
1.1.3 x = −4andx = 6
1.1.5 1. (5/3,∞)
2. [1/7,2/7]
3. (−∞,−3) ∪ (−2,1]
4. (−∞,∞)
5. No solution
6. (−∞,1) ∪ (1,∞)
7. (−2,0) ∪ (2,∞)
8. [4,∞) ∪{0}
9. (0, 1 2 )
10. (−2,−1] ∪ (1,4]
1.1.6 x = − 1 2 and x = − 1 6
1.1.7 1.
(−∞,−2] ∪ [2,∞)
2. [2,4]
3. (−∞,−9/2] ∪
1.2.1 1. (2/3)x +(1/3)
2. y = −2x
3. y =(−2/3)x +(1/3)
4. y = −x/3 + 17/3
5. y = −1/2x + 5/2
1.2.2 1. y = 2x + 2, 2, −1
2. y = −x + 6, 6, 6
3. y = x/2 + 1/2, 1/2, −1
[−1/2,∞)
4. (4,∞)
5. (−∞,∞)
6. (−9,−6) ∪ (4,7)
1.2.4 y = 0, y = −2x + 2, y = 2x + 2
1.2.5 y =(9/5)x + 32, (−40,−40)
1.2.6 y = 0.15x + 10
1.2.7 0.03x + 1.2
1.2.8 (a) P = −0.0001x + 2
(b) x = −10000P+ 20000
1.2.9 (2/25)x − (16/5)
1.2.10 1. 2
√
2. 2
√
3. 2
1.2.12 1. x 2 + y 2 = 9
2. (x − 5) 2 +(y − 6) 2 = 9
3. (x + 5) 2 +(y + 6) 2 = 9
1.2.14 1. circle
2. ellipse
3. horizontal parabola
1.2.15 (x + 2/7) 2 +(y − 41/7) 2 = 1300/49
1.3.1 2nπ − π/2, any integer n
1.3.2 nπ ± π/6, any integer n
1.3.4 − 5 4
1.3.5 sinθ = −x/ √ x 2 + 1, cosθ = −1/ √ x 2 + 1.
1.3.6 − 2π 7
is the unique answer
569