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112-115. Functions from higher derivatives Find the function F that satisfies the following differential equations and initial conditions. 112. F(x) = 1; F'(0) = 3, F(0) = 4 113. F(x) = cos x; F'(0) = 3, F(T) = 4 114. F(x) = 4x; F(0) = 0, F0) = 1, F(0) = 3

112-115. Functions from higher derivatives Find the function F that satisfies the following differential equations and initial conditions. 112. F(x) = 1; F'(0) = 3, F(0) = 4 113. F(x) = cos x; F'(0) = 3, F(T) = 4 114. F(x) = 4x; F(0) = 0, F0) = 1, F(0) = 3

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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Explorations and Challenges 112-115. Functions from higher derivatives Find the function F that satisfies the following differential equations and initial conditions. 112. F(x) = 1; F'(0) = 3, F(0) = 4 113. F(x) = cos x; F'(0) = 3, F(π) = 4 114. F(x) = 4x; F(0) = 0, F0) = 1, F(0) = 3 115. F(x) = 672x5 +24x; F(0) = 0, F'(0) = 2, F(0) = 1 116. Mass on a spring A mass oscillates up and down on the end of a spring. Find its positions relative to the equilibrium position if its acceleration is a(t) = 2 sin t and its initial velocity and position are v(0) = 3 and s(0) = 0, respectively. 117. Flow rate A large tank is filled with water when an outflow valve is opened 0. Water flows out at a rate, in gal/min, given by Q'(t) = 0.1(100 – t²), for 0 ≤ t ≤ 10. at t = ank oftor &
Transcribed Image Text:Explorations and Challenges 112-115. Functions from higher derivatives Find the function F that satisfies the following differential equations and initial conditions. 112. F(x) = 1; F'(0) = 3, F(0) = 4 113. F(x) = cos x; F'(0) = 3, F(π) = 4 114. F(x) = 4x; F(0) = 0, F0) = 1, F(0) = 3 115. F(x) = 672x5 +24x; F(0) = 0, F'(0) = 2, F(0) = 1 116. Mass on a spring A mass oscillates up and down on the end of a spring. Find its positions relative to the equilibrium position if its acceleration is a(t) = 2 sin t and its initial velocity and position are v(0) = 3 and s(0) = 0, respectively. 117. Flow rate A large tank is filled with water when an outflow valve is opened 0. Water flows out at a rate, in gal/min, given by Q'(t) = 0.1(100 – t²), for 0 ≤ t ≤ 10. at t = ank oftor &
91-96. Velocity to position Given the following velocity functions of an object moving along a line, find the position function with the given initial position. 91. v(t) = 2t + 4; s(0) = 0 92. v(t) = et + 4; s(0) = 2 93. v(t) = 2√t; s(0) = 1 94. v(t) = 2 cos t; s(0) = 0 95. v(t) = 6t² + 4t − 10; s(0) = 0 96. v(t) = 4t + sin t; s(0) = 0
Transcribed Image Text:91-96. Velocity to position Given the following velocity functions of an object moving along a line, find the position function with the given initial position. 91. v(t) = 2t + 4; s(0) = 0 92. v(t) = et + 4; s(0) = 2 93. v(t) = 2√t; s(0) = 1 94. v(t) = 2 cos t; s(0) = 0 95. v(t) = 6t² + 4t − 10; s(0) = 0 96. v(t) = 4t + sin t; s(0) = 0
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