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Calculus and Analysis

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.


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=(

Laplace Transform

Find the inverse Laplace transform of (s^3+s^2+2/s) / [s^2(s^2+3s+2)] Using this (or otherwise), Find the solution of the equation y"+3y'+2y = 1-t Find the transform of the following functions: f(t) = (1+t^2)[u(t-1)-u(t-2)] where u(t) is the unit step function. f(t) = sin(t) for 0<t<Pi and f(t)=0 for Pi<t<2*Pi

Diff. EQ

Solve for variable y in terms of t W/ given initial condition: dy/dt + 4y = 40sin3t y(0)=6

Differential Equations

Solve y in terms of t with initial conditions given. a.) (d^2)y/dt^2+3dy/dt+2y=24e^-4t y(0)=10 y'(0)=5 b.) (d^2)y/dt^2+6dy/dt+9y=0 y(0)=10 y'(0)=0

Ln 2 = 1 - 1/2 +1/3 - 1/4 ...

Use 1) sum of (x ^ (n +1))/ (n +1 ) converges uniformly on [-1, 0] 2) sum of x ^ n converges uniformly on (-1, 0] 3) sum of x ^ n = 1/(1-x) to show that ln 2 = 1 - 1/2 + 1/3 - 1/4 ...

Find the Initial Value

4. For the initial value problem dy/dx = 3y^(2/3), y(2) = 0, (a) does existence uniqueness Theorem 1 imply the existence of a unique solution? Explain. (b) Which of the following functions are solutions to the above differential equation? Explain. (b_1) y(x) = 0 (b_2) y(x) = (x - 2)^3 (b_3) y(x) = (x - alpha)^3, x <