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Calculus and Analysis

Differenetial equation

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

Exponential order

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

Laplace transforms

Solve (see in attachment) without using partial fraction decompositions. Thanks you

Quadratic 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

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.

Convolution

Using covolution, find the solution of the differential eq y"+4y'+13y=(1/3)e^(-2t)sin3t y(0)=1, y'(0)=-2

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

Homogeneous Solutions and Differential Equations

Given that the differential equation y^n + p(x)y' + q(x)y = r(x) attached has three solutions of sin x, cos x and sin 2x. Find yh (yh is the corresponding homogeneous solution). See attachment for better formula representation.

Wronskian Solution and Differential Equations

Given that the differential equation y^n + p(x)y' + q(x)y =0 has two solutions x^2 -x and x^3 - x. Use the Wronskian to find p(x). See attachment for better formula representation.

Calculus Help

I attached the problems that I would like you to do. I have already completed these problems by myself, but would like to see if I did them correctly and would like to compare your answers with mine so that I know which problems I mastered and which I need to study up on. Thank you.

Vector Functions to Partial Derrivative

Attached is more clear 1. Distance from a a point to a curve: Find the shortest distances between the point (1,2,1) and a point on the curve r(t)= (1/t*i)+(lnt(t)*j)+(sqrt(t)*k) 2. Distance from a point to a curve: Find the maxmium distances from the point (1,2,-1) to a point on the curve of intersection of the plane z=(