Let v(t) = 2t² + 3t, a = 0 and b = 4, find the distance travelled by a particle moving with velocity v(t) during the time interval by finding: (b-a) (a) tk = a + 2k1 2n (b) v (tk) = v v (a + 2k1 27 ²¹ (b-a)) 2n n n 2k1 (c) 2 = (fe) - Σv (a + 24 m ¹ (0-0) v V 2n k=1 k=1 (d) [v (tk) At = b = a £v - ª £v n k=1 2k1 (a + ²-¹ (8-)) a+ 2n 2k- 1 (e) lm (6) - Im v(a + 22-¹ (-a) (tk) At = lim 2n k=1 b-a n

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Let v(t) = 2t² + 3t, a = 0 and b 4, find the distance travelled by a particle
moving with velocity v(t) during the time interval by finding:
2k1
2n
(b-a)
(a) tk = a +
2k-1
v ( a + ² k = ¹ (b − ₁
-a))
2n
(b) v (tk) = V
n
n
2k1
(e) v (6) -- (+26-¹(b-a)
2n
k=1
k=1
2k
(d) Σv (6) 4 = = v(a + 26-1(b-a))
At n
k=1
k=1
(e) lim Σv (fk) Δt
k=1
= lim
n→∞0
2k - 1
ª Σv (a +²42 - ¹ (b − a))
n
2n
k=1
b-a
Transcribed Image Text:Let v(t) = 2t² + 3t, a = 0 and b 4, find the distance travelled by a particle moving with velocity v(t) during the time interval by finding: 2k1 2n (b-a) (a) tk = a + 2k-1 v ( a + ² k = ¹ (b − ₁ -a)) 2n (b) v (tk) = V n n 2k1 (e) v (6) -- (+26-¹(b-a) 2n k=1 k=1 2k (d) Σv (6) 4 = = v(a + 26-1(b-a)) At n k=1 k=1 (e) lim Σv (fk) Δt k=1 = lim n→∞0 2k - 1 ª Σv (a +²42 - ¹ (b − a)) n 2n k=1 b-a
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