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Calculus and Analysis

Sub Numbers and Geometric Series

(See attached file for full problem description).

Determining where function is continuous

(See attached file for full problem description) f(x)=x+[|x^2|]-[|x|]

Four-step process to find slope predictor function

Please see attached file for full problem description. As you can see I understand the format but not how to substitute the values from the original equation and then simplify.

(a) the position function of the mass, (b) the period of the vibration, and (c) the frequency of the vibration.

A mass of 25g is attached to a vertical spring with a spring constant k = 3 dyne/cm. The surrounding medium has a damping constant of 10 dyne*sec/cm. The mass is pushed 5 cm above its equilibrium position and released. Find (a) the position function of the mass, (b) the period of the vibration, and (c) the frequency of the v

An open-top box is to be made as follows...

(See attached file for full problem description with diagram) An open-top box is to be made as follows: squares of a certain size will be cut away from each of the four corners of a 20" x 30" rectangle, and the ends will be folded upward to form the corner seams, as shown. How big should the square cutouts be in order to maxi

Supply and Demand Functions and Equilibrium

For the demand function d(x)=12.48-.005x^2 and the supply function s(x)= square root of x a) Determine the equilibrium point. Sketch the graph of the demand and supply functions on the same set of axes showing the equilibrium point and the area of the graphs which are the consumers' surplus and producers' surplus. b) De

Solving First Order Differential Equations using the Euler Method

In the problem, use Euler's method to obtain a four decimal approximation of the indicated value. Carry out the recursion of (3) by hand, first using h = 0.1 and then using h = 0.05. y' = 2x - 3y + 1, y(1) = 5; y(1.2)

Solving Differential Equations Word Problems and Initial-Value Problems (12 Problems)

1. Find a general solution of the differntial equation Then find a particular solution that satisfies the intiial condition . 2. A bacteria population is incresing according to the natural growth formula and numbers 100 at 12 noon and 156 at 1 p.m. Write a formula giving after hours. 3. Apply Euler's method to th

Limits Proof : Assume An=[-1/6+ 1/(n+1), 1/(n+2). Calculate lim An or prove it does not exist.

Assume An=[-1/6+ 1/(n+1), 1/(n+2). Calculate lim An or prove it does not exist.

Water Level in Containers - Differential Equations

Water level in containers - Differential equations. See attached file for full problem description.

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 +

Explain equivalent vectors

Explain why vectors QR and RQ are not equivalent. Explain in your own words when the elimination method for solving a system of equations is preferable to the substitution method.

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

Functions/Equations/Calculus

I am looking for assistance with a hodgepodge of problems in which we were asked to answer. I have attempted to provide answers however I am turning for clarification for correctness and/or if missed any information and also how/what is meant by graphing the information within the task. I am going to assume this is the asympto

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

Please solve using Maple 10 and include all data and graphs

Using maple 10: Given the curve: f(x,y)=12+10y-2x^2-8xy-y^4 a. Find the critical points correct to 3 decimal places b. Classify the critical Points cf. Generate and graph; identify the highest point on the graph

(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 &#8730;(t+1) gallons per minute for 0 &#8804; r &#8804; 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

Lagrange Multipliers: Example Problem

The plane 4x-3y+8z=5 intersects the cone Z^2=x^2 + y^2 in an ellipse a. Graph the plane, cone and ellipse b. Use Lagrange multipliers to find the highest and lowest points on the ellipse. This problem must be solved using maple 10 (or 9) please show all work and data entries and outputs.

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