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Calculus and Analysis

Using theorems to determine derivative

(See attached file for full problem description) Using the fundamental theorem of calculus and chain rule, For example, letting the expression equal F(x), and G(u) So for 1) we would have F(x)=G(x ) By the chain rule, dF/dx(x)=(dG/du)|u= x (du/dx) =(1/ | u=x ) (2x) =2x// Determine the derivative: 1) d/dx

Finding implicit form from differential equations

1. find the solution of the initial-value problem: dy/dx = (sin(3x))/(2+cos(3x)), y=4 when x=0 using equation: (f'(x))/(f(x)) dx = ln(f(x)) +c (f(x) > 0) when integrating. 2. a. find in implicit form, the general solution of the differential equation: dy/dx = (4y^(1/2)(e^-x -e^x))/ ((e^x +

Operations management: Process flow chart for Bayside general hospital

Bayside General Hospital is trying to streamline its operations. A problem-solving group consisting of a nurse, a technician, a doctor, an administrator, and a patient is examining outpatient procedures in an effort to speed up the process and make it more cost effective. Listed here are the steps that a typical patient follows

Matlab: Series Solutions to Differential Equations

See the attached files. Instructions for this posting ? All calculations must be shown and all steps must be motivated. A correct answer without the necessary detailed explanation will not earn full marks. Therefore I will not accept the response. ? Please plot all graphs in MATLAB. If you do not have MATLAB then you may u

College Math

Describe a real world situation that could be modeled by a function that is increasing, then constant, then decreasing. What would be the difficulties associated with modeling this situation?

Calculus Periodic Functions

1. A function f(z) is said to be periodic with a period a, a is not equal to zero. if f(z+ma) =f(z), where m is an integer different from zero. prove that a function, which has two distinct periods say, a and b which are not integer multiples of the other- can not be regular in the entire complex plane. Note: Doubly p

Three dimension line

1. A corporation manufactures a product at two locations. The cost of producing x units at a location one and y unites at location two are C1(x)=.01x^2 + 2x + 1000 and C2(y)=.03y^2 + 2y + 300, respectively. If the product sells for $14 per unit, find the quantity that must be produced at each location to maximize the profit P(

Differential Equations : Tangents and Solutions

Consider the differential equation (dy/dx) = (-xy^2)/2. Let y=f(x) be the particular solution to this differential equaiton with the initial condition f(-1)=2. a) On the axis provided sketch a slope field for the given differential equation t the twelve points indicated. (the x-axis goes from -1 to 2 and the y-axis goes from

Calculus for Business Marginal Costs

(See attached file for full problem description) --- 10. y = √x + 3 (√x+3 is all squared). Please use the Chain Rule 16. f (w) = w √w + w² (√w is only squared) Please use the Chain Rule 18. y = 4x³ - 8x² Please use the Chain Rule 5x 46. Margi

Derivatives and Differential Equations and Leaking Tank Word Problem

Water is pumped_into an underground tank at a constant rate of 8 gallons per minute. Water leaks out of the tank at the rate of √(t+1) gallons per minute for 0 ≤ r ≤ 120 minutes. At time t = 0, the tank contains 30 gallons water. (a) How many gallons of water leak out of the tank from time r = 0 to r = 3 minut

Derivatives, Polynomials, Points of Inflection and Equations

See the attached file. 4. Let h(x) be a function defined for all ... such that h(4) = ?3 and the derivative of h(x) is given by .... (a) Find all values of x for which the graph of Ii has a horizontal tangent, arid determine whether 1 has a local maximum, a local minimum, or neither at each of these values. Justify your answer

Conditionally Convergent Series

Prove that if Series An (small "a", sub "n") is a conditionally convergent series and r is any real number, then there is a rearrangement of Series An whose sum is r. [Hints: Use the notation of Exercise 39 (I'll show below). Take just enough positive terms An+ so that their sum is greater than r. Then add just enough negati

Turbulent Boundary Layers, Flow Veolcity, Laminar Flow and Hydraulic Radii

1. DERIVE EQUATION 6-15 2. DERIVE EQUATION 6-48 AND 6-54 3. SOLVE ALL PROBLEMS SHOWN BELOW: 67. Water at 20°C flows through a smooth pipe of diameter 3 cm at 30 m3/h. Assuming developed flow, estimate (a) the wall shear stress (in Pa), (b) the pressure drop (in Pa/rn), and (c) the centerline velocity in the pipe. What is the

Functions and calculus

(See attached file for full problem description) --- 1) Consider the following function: a) f (x) = 9x2 - x3 b) f (x) = x + 1 x - 2 c) f (x) = x2/3 (x - 5) for each of the above functions complete the following table. Show the work to justify your answers below the table. f(x) is i

Locus: Two Trees Located at Grid Points

In a backyard, there are two trees located at grid points A(-2,3) and B(4,-6). a) The family dog is walking through the backyard so that it is at all times twice as far From A as it is from B. Find the equation of the locus of the dog. Draw a graph that shows the two trees, the path of the dog. and the ralationship defining

Calculus for Business:

3) A wholesaler that sells computer monitors finds that selling price "p" is related to demand "q" by the relation p=280 - .02q where p is measured in dollars and q represents number of units sold a. Find the wholesaler's Revenue function as a function of q, using Revenue = (price) (quantity) b. Find the expression for Mar

Stochastic Differential Equations, Density Functions and Random Variables

We use the notation X ~N(μ, σ2) to indicate that the density function for the continuous random variable X, fx(x), has the form .... (a) If X ~N(μ, σ2) show that..... (Hint: you will need to know how to find the density function for X ? μ from the density function for X). (b) If ...., and X1 and X2 a

Sturm-liouville problem

1. (a) Find the eigenvalues and eigenfunctions of the boundary-value problem. x2y'' + xy' + λ y = 0, y(1) = 0, y(5) = 0. (b) Put the differential equation in self -adjoint form. (c) Give an orthogonality relation. 2. Hermite's differential equation y'' -2xy' + 2ny = , n =

Differential Equations : Equations of Motion, Laplace Transforms

Refer to figure 2 in attachment. a) Write the equations of motion for the mechanical system.****PLEASE SHOW YOUR FREE-BODY FOR EACH MASS****THANKS B) Take the Laplace transform of these equations, arrange them in matrix form, solve for the displacement x2(t), and find the transfer function T(s)= X1(s)/F(s) C) Using the co

Limits and L'Hopital's Rule (34 Problems with High Quality Solutions)

Find the limits using L'Hopital's rule where appropriate. If there is a more elementary method, consider using it. If L'Hospital's rule does not apply explain why. 1) lim as x approaches -1 (x^2 -1) / (x + 1) 2) lim as x approaches -1 (x^9 -1) / (x^5 - 1) 3) lim as x approaches -2 (x+2) / (x^2 +3x + 2) 4) lim as x approa

Graphing, Translation, Reflection, Domains, Limits, Derivatives

For the following graph the given functions on a computer screen, how are these graphs related? 1) Y=2^x, y=e^x, y=5^x, y=20^x 2) Y=3^x, y=10^x, y=(1/3)^x, y=(1/10)^x _______________________________________________________________________ Make a sketch of the function. 7) y=4^x-3 8) y=-2x^-x 9) y=3-e^x 13)

Inverse function Values

Please solve each problem with a detailed solution showing each step to solve the problem. Since the symbols confuse me at times please use "baby" math to show how to get from the start to the end. I understand the book in some ways, but the more I see completed the better I can think about the rest of the problems I need to d