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5. (a) Let f(x) = 3 Find the area between the of graph y = f(x) and the x-axis r(lnx + 3)² for e≤ x <∞.

5. (a) Let f(x) = 3 Find the area between the of graph y = f(x) and the x-axis r(lnx + 3)² for e≤ x <∞.

Calculus: Early Transcendentals
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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3 x(lnx + 3)2* 5. (a) Let f(x) = for e≤ x <∞o. (b) Let g(x) = Find the area between the of graph y = f(x) and the x-axis 3 x(lnx+3)² + x2023. Show that the area between the graph of y = g(x) and the x-axis for e< x < oo is finite. Hint. Notice it's not asking what the area is, it's just asking to show it is finite.
Transcribed Image Text:3 x(lnx + 3)2* 5. (a) Let f(x) = for e≤ x <∞o. (b) Let g(x) = Find the area between the of graph y = f(x) and the x-axis 3 x(lnx+3)² + x2023. Show that the area between the graph of y = g(x) and the x-axis for e< x < oo is finite. Hint. Notice it's not asking what the area is, it's just asking to show it is finite.
6. Suppose an astronaut brings back a radioactive substance from the moon, which decays over time. It takes 3 days for the astronant to return to earth from the moon. When they get back to earth, they immediately determine the mass of a sample of the substance is 200 grams. Twenty days later, the mass has decayed to 180 grams. Assume the rate of change of the substance's mass at time t is proportional to the mass of the object at time t (for all t, including the journey from the moon). You can use your calculator to give decimal approximations for your final answers for both parts (round your final answer to one decimal place). (a) How long will it take for the sample to decay from 200 grams to 100 grams? (This is called the half life of the substance.) (b) What was the mass of the sample when the astronaut left the moon? (b) The your answer to
Transcribed Image Text:6. Suppose an astronaut brings back a radioactive substance from the moon, which decays over time. It takes 3 days for the astronant to return to earth from the moon. When they get back to earth, they immediately determine the mass of a sample of the substance is 200 grams. Twenty days later, the mass has decayed to 180 grams. Assume the rate of change of the substance's mass at time t is proportional to the mass of the object at time t (for all t, including the journey from the moon). You can use your calculator to give decimal approximations for your final answers for both parts (round your final answer to one decimal place). (a) How long will it take for the sample to decay from 200 grams to 100 grams? (This is called the half life of the substance.) (b) What was the mass of the sample when the astronaut left the moon? (b) The your answer to
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