A rocket is departing Earth towards Mars. The following function represents the rocket's vertical velocity for the first 3 hours: v(t) = t - t²e²² in km/h. (a) Approximate the distance travelled by the rocket in the first 3 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 3 hours: Distance km. (d) Calculate the exact distance travelled by the rocket in the first 3 hours: Distance = km. km.
A rocket is departing Earth towards Mars. The following function represents the rocket's vertical velocity for the first 3 hours: v(t) = t - t²e²² in km/h. (a) Approximate the distance travelled by the rocket in the first 3 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 3 hours: Distance km. (d) Calculate the exact distance travelled by the rocket in the first 3 hours: Distance = km. km.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 74E
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Question
Ee.84.
![A rocket is departing Earth towards Mars. The following function represents the rocket's vertical velocity for the first 3 hours:
v(t) = t
- t²e¹² in km/h.
(a) Approximate the distance travelled by the rocket in the first 3 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 3 hours:
Distance
km.
(d) Calculate the exact distance travelled by the rocket in the first 3 hours:
Distance =
km.
km.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff45f8a2a-f450-4d14-a99f-85887de7a617%2Fc4727a7b-27da-479f-8ab9-144f76cd08fd%2Fvrtk85_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A rocket is departing Earth towards Mars. The following function represents the rocket's vertical velocity for the first 3 hours:
v(t) = t
- t²e¹² in km/h.
(a) Approximate the distance travelled by the rocket in the first 3 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 3 hours:
Distance
km.
(d) Calculate the exact distance travelled by the rocket in the first 3 hours:
Distance =
km.
km.
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