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    Calculus and Analysis

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    Indicated Scalar and Vector Surface Integrals

    Please see the attached file for full problem description. Let S denote the closed cylinder with bottom given by z=0, top given by z=4, and lateral surface given by the equation x^2 + y^2 = 9. Orient S with outward normals. Determine the indicated scalar and vector surface integrals.

    Linear Homogeneous Partial Differential Equation

    Find the General Solution of the equations. (a) r = a2t (b) r - 3as + 2a2t = 0 where r = ∂2z/∂x2 , s = ∂2z/∂x∂y, t = ∂2z/∂y2 (c) (2D2 + 5DD′ + 2D′2)z = 0 (d) ∂3z/∂x3 - 3∂3z/∂x2∂y + 2∂3z/∂x∂y2 = 0

    Differential Equation Solution

    I am having difficulties gaining a solution for the following differential equation of x'=2t3 -6t2 + t1/2. Could I please get assistance with detailing my solution.

    The Method of Lagrange Multipliers

    Use the method of Lagrange multipliers to find the indicated extremum. You may assume the extremum exists. Find the maximum and minimum values of f(x,y,z) = x + 3y - z subject to z = 2x^2 + y^2

    Critical points sample question

    F(x,y)= xy + 8/x + 8/y Find the critical points of the given function and classify each as relative min., relative max., or a saddle point.

    Finding Critical Numbers; Finding the Extrema in the Interval

    1. Find all the critical numbers: . 2. Find all the extrema in the interval [0,2 ] for . 3. Find the absolute maximum and the absolute minimum on the interval (1,4]. 4. State why Rolle's Theorem does not apply to the function on the interval [-2,0]. 5. Find all relative extrema of , include the designation of maxim

    Laplace Transform

    Please see the attached file for the fully formatted problem. Find L[(sin t)/t].

    Exponential order

    Show that equation is of exponential order and not of exponential Order. (please see attachment for details)

    Laplace Transform

    Find the Laplace transform of: f(t) = exp(2t) for 0<t<3 and 0 everywhere else. See attached file for full problem description.

    Tunnel word problem

    Before starting, the answer to the 2nd problem is NOT y=3.9x+20 or y=4.1x-300. Those are the solutions to the first part of the question. The second part is asking for the TOTAL cost when you have "x" amount of feet, not just the cost of digging ONE foot. I posted earlier and received the above answers. The question I would like

    Finding a maximum point of a function

    The total profit in dollars for the sale of n microwave ovens is given by p=-2n^2+140n-174 what value of n will provide the maximum profit. Please show all work including the line graph.

    Properties of a parabola

    Find the domain, range and x intercepts of the following problem approximate to two decimal places of the function y=3x^2-30x+5

    Word Problem on Work in Joules

    Dont really want you to give me answer, just thoery on how to complete these type of problems. Word problem with calculus Thank You (See Attached)

    Calculus/ For OTA 103997 only

    Please respond with a Microsoft Word document. Thank you. Please see attachment for actual questions and full formulas. 1. Decide whether Rolle's Theorem can be applied to on the interval [-1,3]. If Rolle's Theorem can be applied, find all the values, c, in the interval such that . If Rolle's Theorem cannot be a

    Series of Calculus Questions

    Please respond with a Microsoft Word document with the answers written in standard text. Thank you. Series of Various Calculour Questions Attached. You do not need to show your work for this one because I would simply like to compare your answers with mine so that I am sure that I did everything correct on mine. Please ju

    Laplace Transform function

    Find the Laplace Transform of the following function f(t)=(t^2-3t+2)u(t-1)-(t^2-3t+2)u(t-2) Thank you for your time and help!

    Forced harmonic oscillator

    Consider the forced harmonic oscillator: y'' + by' + ky = g(t) + y0 where the forcing is made up of two parts, constant forcing (y0) and forcing (g(t)) that changes over time. a) Let w(t) = y(t) - y0/k. Rewrite the forced harmonic oscillator equation in terms of the new variable w. b) In what ways are the solutions of the t