Consider the piecewise defined function w(t) modeling the rate at which sand enters a container, and the differentiable function G(t) modeling the rate at which sand leaves the container. Both functions are measured in L/hr and at t = 1 hour there are 500 L in the container. 61 + 4, 1>2 w( 1) = | 3cos( 51 – 10) + 13, Osis2 1 4 9 12 G(0), Lhr 10 8 15 22 a) Is w(t) continuous att = 2? Is w(t) differentiable at t = 2? Justify your answer. b) Use a right Riemann sum with two subintervals indicated by the chart to approximate the amount of sand that has exited the container on 1sts 9. Show your process. c) Is the amount of sand in the tank increasing or decreasing at t = 4. Give a reason for your answer. d) Using Mean Value Theorem yields the approximation for G'(2.5) z. Using correct units, explain the meaning of this value in the context of the question. e) Evaluate Í w(t)dt. Show your process. (remember don't simplify) f) Write an equation that would represent the time K when the container has 545 L of sand in it. Do not solve. g) Consider the function given by h'(t) = w(t) + G(t) and give the second degree Taylor polynomial centered at t = 4 for h(t). It is known that h(4) = 20 and G'(4) = -9. h) Write an expression for the length of w(t) from t = 0 to t = 2. Do not solve. i) Find an antiderivative that could be used to evaluate t - G"(t)dt .
Consider the piecewise defined function w(t) modeling the rate at which sand enters a container, and the differentiable function G(t) modeling the rate at which sand leaves the container. Both functions are measured in L/hr and at t = 1 hour there are 500 L in the container. 61 + 4, 1>2 w( 1) = | 3cos( 51 – 10) + 13, Osis2 1 4 9 12 G(0), Lhr 10 8 15 22 a) Is w(t) continuous att = 2? Is w(t) differentiable at t = 2? Justify your answer. b) Use a right Riemann sum with two subintervals indicated by the chart to approximate the amount of sand that has exited the container on 1sts 9. Show your process. c) Is the amount of sand in the tank increasing or decreasing at t = 4. Give a reason for your answer. d) Using Mean Value Theorem yields the approximation for G'(2.5) z. Using correct units, explain the meaning of this value in the context of the question. e) Evaluate Í w(t)dt. Show your process. (remember don't simplify) f) Write an equation that would represent the time K when the container has 545 L of sand in it. Do not solve. g) Consider the function given by h'(t) = w(t) + G(t) and give the second degree Taylor polynomial centered at t = 4 for h(t). It is known that h(4) = 20 and G'(4) = -9. h) Write an expression for the length of w(t) from t = 0 to t = 2. Do not solve. i) Find an antiderivative that could be used to evaluate t - G"(t)dt .
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Concept explainers
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
Topic Video
Question
Help with parts D E F G H I
Transcribed Image Text:Consider the piecewise defined function w(t) modeling the rate at which sand enters a container,
and the differentiable function G(t) modeling the rate at which sand leaves the container. Both
functions are measured in L/hr and at t = 1 hour there are 500 L in the container.
I> 2
3cos( 51 – 10) + 13, 0<1<2
|1 4 9 12
G), L/hr 10 8 15 22
t
61 + 4,
w( t) =
a) Is w(t) continuous at t = 2? Is w(t) differentiable at t = 2? Justify your answer.
b) Use a right Riemann sum with two subintervals indicated by the chart to approximate the
amount of sand that has exited the container on 1sts 9. Show your process.
c) Is the amount of sand in the tank increasing or decreasing at t = 4. Give a reason for your
answer.
d) Using Mean Value Theorem yields the approximation for G'(2.5) . Using correct
units, explain the meaning of this value in the context of the question.
3
e) Evaluate Í w(t)dt. Show your process. (remember don't simplify)
1
f) Write an equation that would represent the time K when the container has 545 L of sand in it. Do
not solve.
g) Consider the function given by h'(t) = w(t) + G(t) and give the second degree Taylor polynomial
centered at t = 4 for h(t). It is known that h(4) = 20 and G'(4) = -9.
h) Write an expression for the length of w(t) from t = 0 to t = 2. Do not solve.
i) Find an antiderivative that could be used to evaluate į t - G"(t)dt.
a
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
