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
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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Show all work, thank you! (Question 114 and 96)
![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 &](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ea0963c-64ff-46a6-b97c-79944ef211ae%2F751ec4f0-ead4-4ab0-81dd-0b4411e63086%2F1y5550q_processed.jpeg&w=3840&q=75)
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ea0963c-64ff-46a6-b97c-79944ef211ae%2F751ec4f0-ead4-4ab0-81dd-0b4411e63086%2F6dpu7v_processed.jpeg&w=3840&q=75)
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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