Solutions Manual for University Calculus Early Transcendentals 3rd Edition by Hass Full download: http://downloadlink.org/p/solutions-manual-for-university-calculus-earlytranscendentals-3rd-edition-by-hass/ Test Bank for University Calculus Early Transcendentals 3rd Edition by Hass IBSN 9780321999573 Full download: http://downloadlink.org/p/test-bank-for-university-calculus-earlytranscendentals-3rd-edition-by-hass-ibsn-9780321999573/
CHAPTER 2 2.1
LIMITS AND CONTINUITY
RATES OF CHANGE AND TANGENTS TO CURVES
Δf f (3)− f (2) = 19 1. (a) Δx = 3−2 = 28−9 1
2. (a)
Δg Δx
=
= 3. (a) Δh Δt
g (3) − g (1) 3 −1
h
Δf f (1) − f (−1) =1 (b) Δx = 1−(−1) = 2−0 2
= 3 − 2−1 = 2 (
)
(b)
( 3π4 )−h( π4 ) = −1−1 = − 4 3π − π 4 4
− g ( −2) 8 − 8 = g (4) = 6 =0 4 − (−2)
h( π ) − h( π ) = 2π π 6 = 0−π 3 = −3 3 (b) Δh Δt π −
π
π 2
Δg Δx
2
Δg g (π )− g (0) (2−1)−(2+1) = = − π2 4. (a) Δt = π −0 π −0
Δg
(b) Δt =
6
g (π )− g (−π ) π −(−π )
3
= (2−1)−(2−1) =0 2π
R (2)− R (0) 1 3−1 = 2−0 = 8+1− = 2 =1 5. ΔR Δθ 2 P (2)− P (1) (8−16+10)−(1−4+5) = 2−2 = 0 = 2−1 = 6. ΔP Δθ 1
7. (a) (b)
Δy Δx
2 2 2 2 2 −5) = ((2+h ) −5)−( = 4+4h +hh −5+1 = 4h +h = 4 + h. As h → 0, 4 + h → 4 at P(2, −1) the slope is 4. h h y − (−1) = 4( x − 2) y + 1 = 4 x − 8 y = 4x − 9
Δy Δx
2 2 2 −3 = −4h−h 2 = −4 − h. As h → 0, −4 − h → −4 at P(2, 3) the slope = (7−(2+h )h )−(7−2 ) = 7−4−4h−h h h is −4. (b) y − 3 = (−4)( x − 2) y − 3 = −4 x + 8 y = −4 x + 11
8. (a)
Δy
((2+ h)2 − 2(2+ h)−3)−(22 −2(2)−3)
4+ 4h + h 2 − 4− 2h −3−(−3)
= 9. (a) Δx = h h P(2, − 3) the slope is 2. (b) y − (−3) = 2(x − 2) y + 3 = 2x − 4 y = 2 x − 7.
2
= 2h+ h = 2 + h. As h → 0, 2 + h → 2 at h
2 1+ 2h+ h −4−4h−(−3) Δy ((1+ h) −4(1+ h))−(1 − 4(1)) = = h −2h = h − 2. As h → 0, h − 2 → −2 at P(1, − 3) the 10. (a) Δx = h h h slope is −2. (b) y − (−3) = (−2)( x −1) y + 3 = −2x + 2 y = −2 x −1. 2
Δy
(2+ h)3 − 23
2
8+12h+ 4h 2 + h3 −8
2
12h +4h 2 +h3
2
2