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# Calculus and Analysis

### Inflection Points

Consider the function f(x)=12x^5+75x^4 -120x^3+1. (It is 12x^5 + 75x^4 -120x^3 + 2). f(x) has inflection points at (reading from left to right) x=D, E, and F Where D is _______ Where E is_______ Where F is________ For each of the following intervals, tell whether f(x) is concave up (type in CU) or concave down (type i

### Lagrange multipliers method

Considering the surface f(x,y)=xy and the constraint x2+y2=1 , answer to the following questions: A. Using the Lagrange multipliers method we can obtain some possible maximum and minimum for ?=ï?±1/2 B. The Lagrange multipliers method is the most convenient C. There are two absolute maximum and two absolute minimum D. Th

### Integral Approximation and Nim Strategy

** Please see the attached file for the complete solution response ** I need a little assistance with a couple of problems. Please include all the work with each problem. Thank you for your assistance. Question 1: Two players take turns removing 1, 2, 3, or 4 objects from a set of 16 identical objects (without replaci

### Maximization of Profit for Canoe Rentals

Imagine that you run a consulting business that helps small businesses with process improvement. Justin runs a small canoe-rental business somewhere in Florida and currently charge \$10.50 per canoe rental. He has an average of 36 rentals per day. With the rising cost he wants to increase the charge for the rental however he want

### Calculus Profit/Product Demand

Please solve the problems: 1. If p is price in dollars and q is quantity, demand for a product is given by q = 5000e^0.08p a. What quantity is sold at a price of \$10? b. Find the derivative of demand with respect to price when the price is \$10 and interpret your answer in terms of demand. 2. The demand for a product is

### Calculus Revenue/Costs/Graphing

Mr. Mick Mouse has a trap company with fixed costs of \$846 variable (ie: operating) costs of \$2 per trap and a demand curve of: traps=116-2(price). Since Mick doesn't understand economics find the revenue and cost functions in terms of price for his business. a) Graph these two functions over the price domain. Find the break

### Calculus: Retirement Plans

A friend wants to know how much money she will have at retirement if she invests \$10,000 compounded continuously in a security that earns interest at ten percent per year. Identify the functional relationship of her balance on-account over time. a) Compute the retirement balance if my friend is currently 50 yrs old and retire

### What would it cost to produce these traps?

Mr. Mick Mouse has a trap company with fixed costs of \$846, variable (i.e. operating) costs of \$2 per trap and a demand curve of: traps=116-2(price). Since Mick does not understand economics, find the revenue and cost functions in terms of price for his business. a) Describe the graph of these two functions over the price do

### Continuously Compounded Rate

See the attached file. 14. The world population of Ferrets has increased at a continuously compounded rate from 20 in 1970 to about 60 in 2000. Develop a mathematical model to forecast population growth in future years. a) Graph the population against time and determine, identify or describe this relationship in your own

### Finding the inverse laplace transform of G(s) = 1/Sqrt(s^2 +1)*F(s) using convolution theorem

Hi there, I have a question which can be located here http://nullspace8.blogspot.com/2011/10/e8_26.html. can someone please take a look? Full working step by step solution in pdf or word please. If you think the bid is insufficient and you can do it, please respond with a counter bid. Thank you.

### Laplace Transform

Hi there, I have a question which can be located here http://nullspace8.blogspot.com/2011/10/e7.html. can someone please take a look? Full working step by step solution in pdf or word please. If you think the bid is insufficient and you can do it, please respond with a counter bid. Thank you.

### Taylor Series ODE

Hi there, I have a question regarding Taylor Series ODE which can be located here http://nullspace8.blogspot.com/2011/10/14.html. can someone please take a look? Full working step by step solution in pdf or word please. If you think the bid is insufficient and you can do it, please respond with a counter bid. Thank you.

### Computing the Mass of a Thin Shell

Hi I have a question on http://none-questions.blogspot.com/2011/10/mm-q18.html Can someone please take a look and provide me a solution in step by step format in pdf or word? If you think the bid is insufficient, please put in a counterbid, thanks

### Solving differential equations..

Please see the attached file for full description. 1. Find both the first and second order differentials (y' and y") for the following functions: 2. Use integrating factor to convert the following equation into "exact ODE" form and solve for y. 2xy' = (y -x) (y + x)/ y 3. Solve the differential equation, y is a functi

### Financial information on Jerry's Jigsaw Puzzles

3. A company, Jerry's Jigsaw Puzzles, has fixed costs of \$5000 and operating costs of \$3 per puzzle. If the price of puzzles is \$6 and currently the company makes 1000 puzzles, does Jerry have a problem? a) Compute Jerry's revenues and costs for every 500 puzzles starting at zero up to the limit of 6000 puzzles and graph bot

### Solve: Looking at Retirement Balances

A colleague wants to know how much money she will have at retirement if she invests \$25,000 in a bank account that yields six percent compounded annually. a) List some possible retirement balances if my friend is currently 50 yrs old. (hint: some folks retire at 60 and some at 62). b) Graph the balance on account against

### Portfolio Management Portfolio Analysis

You observe two portfolios HG and VL with betas of 1.20 and 0.50 and expected return of 9% and 5.5% respectively. a. Calculate the risk free rate and the market risk premium. Write the SML function

### Instantaneous velocity of the ball

If a ball is thrown straight up into the air with an initial velocity of 75 ft/s, it height in feet after t second is given by y=75tâ?'16t^2. Find the average velocity for the time period beginning when t=1 and lasting (i) 0.1 seconds (ii) 0.01 seconds (iii) 0.001 seconds Finally based on the above results, guess wha

### Calculus

Let f(x) = 2x^2+3x+3 and let g(h)=f(3+h)&#8722;f(3). h Determine each of the following: (a) g(1)= (b) g(0.1)= (c) g(0.01)= You will notice that the values that you entered are getting closer and closer to a number L. This number is called the limit of g(h

### Introduction to Ordinary Differential Equations

(e^y + 1)^2 * e^-y dx + (e^x + 1) * e^-x dy = 0 An ordinary differential equation (ODE) is an equation that involves derivatives, but no partial derivatives. The "dx" and "dy" found in the equation denote the derivatives involved. We read these notations as "with respect to x" (dx) and "with respect to y" (dy). Their inclu

### Laplace Transforms

Hi there, I have a question regarding IVP Laplace Transforms which can be located here http://none-questions.blogspot.com/2011/09/d-q24.html. can someone please take a look? Full working step by step solution in pdf or word please. Thank you.

### Finding Inverse Laplace transforms of a function

Finding the inverse Laplace transform of the function X(s) = s/{(s - 2)^1.5.(s^2 + 1)} Using partial fraction expansion and inverse laplace transforms of known functions.

### Deduction of City population Growth

Calculs Population The population of a certain city was 1200 in the year 2000 (a) If the observed growth rate is 2 percent per year, find a function that models the population t years after the year 2000. Your answer is (b) If the observed growth rate is 5000 people per year, find a function that models the population t year

### Second Order Differential Equation - Power Series Solution

Hi there, I have a question regarding Differential Equations which can be located here http://none-questions.blogspot.com/2011/09/d-q7.html. can someone please take a look? Thanks.

### Simulation of Predator-Prey Ecological Model

See the attached file. The predator prey system below has a term for the carrying capacity of the prey species. Initially the prey population N(0) = 330 and the predator population P(0) = 270. dN/dt = 0.07N(700-N) - 0.05NP dP/dt = 0.04PN - 4P (a) In the absence of predators, what is the carrying capacity of the prey'

### limit theorem

Please show complete solution. Continuity 1) The function f:R-{0,2}→R is definied by f(x)=(x^2-4)/(x^3-2x^2 ). Use limit theorems to determine whether f can be defined at 2 such that f is continuous at 2.

### Initial value problem in Differential Equations

The following problem was given as an example by the professor but I can't seem to come up with the same answer as he did. The answer he got was C1 = -2 and C2 = 1/4 I keep getting C1 = - 1/4 and C2 = - 1/2 There are three possibilities 1) He's wrong 2) I'm wrong or 3) we are both wrong. I need to know which it is. Can you

### Fundamental Theorem of Calculus.

Find area under the the graph f(x) =x between x=0 and x=1 by taking the limit of the sum of approximating rectangles whose heights are the values of the function at the right hand end point of each subinterval.

### Determine the shape and equation of the curve given in a parametric form.

2. A curve C has the parametrization x = a sint cos alpha, y = b sint sin alpha , z = c cost , t â?¥ 0 , where a, b , c, alpha are all positive constants. a) Show that C lies on the ellipsoid x^2/a^2+y^2/b^2+z^2/c^2=1 b) Show that C also lies on a plane that contains the z axis. c) Describe the curve C. Give its equatio

### The earth's spherical coordinate system

Consider a rectangular coordinate system with origin at the center of the earth, z-axis through the North Pole, and x-axis through the prime-meridian. Find the rectangular coordinates of Beijing, China (39Ù' 55'N,116Ù' 25'E )degree. A minute is 1/60degree . Assume the earth is a sphere of radius R=6367km. Beijing has coord