A rocket is departing Earth towards Mars. The following function represents the rocket's vertical velocity for the first 4 hours: v(t) = t²e/t³ in km/h. (a) Approximate the distance travelled by the rocket in the first 4 hours using a right-hand Riemann sum with 4 intervals: Distance (b) Approximate the velocity function with a Taylor polynomial of degree 2 centred at a = 0: v(t) ≈+t+t². (c) Use the polynomial approximation to obtain a new approximation of the distance travelled by the rocket in the first 4 hours: Distance km. (d) Calculate the exact distance travelled by the rocket in the first 4 hours: Distance km. km.
A rocket is departing Earth towards Mars. The following function represents the rocket's vertical velocity for the first 4 hours: v(t) = t²e/t³ in km/h. (a) Approximate the distance travelled by the rocket in the first 4 hours using a right-hand Riemann sum with 4 intervals: Distance (b) Approximate the velocity function with a Taylor polynomial of degree 2 centred at a = 0: v(t) ≈+t+t². (c) Use the polynomial approximation to obtain a new approximation of the distance travelled by the rocket in the first 4 hours: Distance km. (d) Calculate the exact distance travelled by the rocket in the first 4 hours: Distance km. km.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A rocket is departing Earth towards Mars. The following function represents the rocket's vertical velocity for the first 4 hours:
v(t)
=
t²e/t³
in km/h.
(a) Approximate the distance travelled by the rocket in the first 4 hours using a right-hand Riemann sum with 4 intervals: Distance
(b) Approximate the velocity function with a Taylor polynomial of degree 2 centred at a = 0:
v(t) ≈+t+t².
(c) Use the polynomial approximation to obtain a new approximation of the distance travelled by the rocket in the first 4 hours:
Distance
km.
(d) Calculate the exact distance travelled by the rocket in the first 4 hours:
Distance =
km.
km.
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