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11. A certain population can be modeled by the differential equation dP dt = -0.1P(100-P), where P(t) represents the population at time t. a) What are the equilibrium solutions of the equation? b) For what values of P is the population increasing? c) For what values of P is the population decreasing? d) Classify all equilibria as stable or unstable. e) If P(0) 15, what is lim P(t)? 100 1 2. a) Use the fact that tan x= dx to find a geometric power series 1+x -1 representation for tan x and find its radius of convergence. Please write your answer using summation notation. b) Estimate tan¯¹ (0.01)=√ series from a). 0.01 1 dt to five decimal places using the power 0 1+t

11. A certain population can be modeled by the differential equation dP dt = -0.1P(100-P), where P(t) represents the population at time t. a) What are the equilibrium solutions of the equation? b) For what values of P is the population increasing? c) For what values of P is the population decreasing? d) Classify all equilibria as stable or unstable. e) If P(0) 15, what is lim P(t)? 100 1 2. a) Use the fact that tan x= dx to find a geometric power series 1+x -1 representation for tan x and find its radius of convergence. Please write your answer using summation notation. b) Estimate tan¯¹ (0.01)=√ series from a). 0.01 1 dt to five decimal places using the power 0 1+t

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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11. A certain population can be modeled by the differential equation dP dt = -0.1P(100-P), where P(t) represents the population at time t. a) What are the equilibrium solutions of the equation? b) For what values of P is the population increasing? c) For what values of P is the population decreasing? d) Classify all equilibria as stable or unstable. e) If P(0) 15, what is lim P(t)? 100
Transcribed Image Text:11. A certain population can be modeled by the differential equation dP dt = -0.1P(100-P), where P(t) represents the population at time t. a) What are the equilibrium solutions of the equation? b) For what values of P is the population increasing? c) For what values of P is the population decreasing? d) Classify all equilibria as stable or unstable. e) If P(0) 15, what is lim P(t)? 100
1 2. a) Use the fact that tan x= dx to find a geometric power series 1+x -1 representation for tan x and find its radius of convergence. Please write your answer using summation notation. b) Estimate tan¯¹ (0.01)=√ series from a). 0.01 1 dt to five decimal places using the power 0 1+t
Transcribed Image Text:1 2. a) Use the fact that tan x= dx to find a geometric power series 1+x -1 representation for tan x and find its radius of convergence. Please write your answer using summation notation. b) Estimate tan¯¹ (0.01)=√ series from a). 0.01 1 dt to five decimal places using the power 0 1+t
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