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Calculus and Analysis

Various Problems in Precalculus

Total of 29 problems that look like these What is the degree of f(x) =3x^6 +4x^2 +x - 1 What is the leading coefficient of f(x) = 3x^6 +x^2 +x - 1 Write a polynomial in simplest form with roots 5i and -5i Solve (x - 1)(x - 2) ? 0 x - 3

Roots Polynomial Functions

There are total of 14 attached problems and they look like these: Find all possible rational roots of: f(x)=2x ^4 - 5x^3 +8x +4x+7 Find all the real roots of f(x) = x^3 + x^2 -8x -6 Find the number of possible positive and negative real zeros of :f (x) = 3x^3 -4x^2 -5x +1. See the attached file.

Concept of minimum/maximum for problem solving.

Hello, I have been studying the concepts of minimums and maximum values. However, I have a word problem that is really giving me a hard time and I would appreciate some assitance so I will know how to go about solving such a problem in the future. * A rectangular hole is to be cut in a wall for a vent. If the perimeter of th

Finding an Equation of the Tangent to the Curve

Find an equation of the tangent to the curve: x = tan (theta), y = sec (theta) at the point (1, sqrt(2)) by two methods: (a) without eliminating the parameter, and (b) by first eliminating the parameter.

Tangent lines at a point

a)Find the slope of the tangent line to the function y=1/sqrt(2x-1) at the point a, using the definition of a derivative. b) At which point does the tangent to the function have a slope of -1 c) Find an equation of the tangent line at the point in (b)

Two Separable Differential Equations

Please find the attached. i) x ̇=-(t+1)x/t ii) x ̇=-t^3/(x+1)^2 a) Find all the solutions of i) and ii). b) for i) and ii) Discuss/Give possible choices for a domain B⊂R^2 such that the IVP with x(t_0 )=x_0 has a unique solution.

Derivative as an Instantaneous Rate of Change

The value (in thousands of dollars) of a certain car is given by the function V=48/t+3 where t is measured in years. Find a general expression for the instantaneous rate of change of V with respect to t and evaluate this expression when t =3 years. Will the general expression be -48/(t+3)^2, and the rate change -$1300/year?

Solutions to First-Order Ordinary Differential Equations

Question 1: (1 points) Solve the following equations for given initial condition. Please represent your answer in the implicit form ( ). Use y(x) instead of y Question 2: (1 points) Integrate the following equations and write a solution for given initial condition. Please represent your answer in the implicit form

Calculus Compound Interest/Principle

A friend, who is currently 40 years old, wants to know how much money she will have at retirement if she invests $5,250 every year in a fund that ears 8% per year. a. List the balance on the account for the first three years of the fund if interest is compounded continuously. b. Graph the balance on account against time and

Calculus: Best Fit Lines and Prediction

See the attached files. Consider the weight of a pet ferret recorded over the first six months of life: Age 0 1 2 3 4 5 6 Weight .69 1.09 1.38 1.61 1.79 1.94 2.08 A. Graph the ferret weights on age and find a mathematical expression that relates weight of a ferret as a function of age. Compute how much weight a ferret

Calculus: Lower and Upper Estimates

Roger decides to run the marathon. His friend follows in a car and clocks his speed in mph. Roger stops after an hour and a half but his friend keeps the following records: 1. Calculate upper and lower estimates for the distance the two have traveled from the starting gate. 2. If he started at 8am could Roger have walked t

Metabolizing Drugs

People metabolize drugs at specific rates. For example, caffeine has a half-life of about four hours. Determine a functional relationship between caffeine (in milligrams) in your system and your last cup of java. (Each cup has 80 mgs). a. Graph the function for time= 1, 2, 3, 4, 5 and 6 hours since your last cup. What is th

Forecasted Revenue for Harley-Davidson

Please help with the following problems. Homework Set 17: Problem 4 Section 6.3, Problem 5 Section 6.3, Problem 6 Section 6.3 Section 6.3: Problem 4 pg. 288 13. Harley-Davidson Inc. manufactures motorcycles. During the years following 2003 (the company's 100th anniversary), the company's net revenue came be approxima

Estimate the total solar PV production between 2000 and 2010.

Homework Set 15: Problem 10 Section 5.4, Problem 11 Section 5.4 Section 5.4: Problem 10 pg. 257 10. World annual natural gas consumption, N, in millions of metric tons of oil equivalent, is approximated by N= 1770 + 53t, where t is in years since 1990. A. How much natural gas was consumed in 1990? In 2010? B. Esti

Estimate total oil consumption during this 25-year period

Homework Set 13: Problem 8 Section 5.1, Problem 12 Section 5.1 Section 5.1: Problem 8 pg. 239 8. The following table gives world oil consumption, in billions of barrels per year. Estimate total oil consumption during this 25-year period. Year 1980 1985 1990 1995 2000 2005 Oil (bn barrels/year) 22.3 21.3 23.9 24.9 27

Particle velocity and harmonic motion

You are in your Physics lab and your professor has an experiment set up to help you learn about harmonic motion. The set up is that you have 112.5/pi^2 (approxmately 11.39 kg) on a frictionless surface that is attached to a spring constant 12.5 N/m. You pull the block to 3/pi meters (approximately .955 meters) such that x(0) = 3

Finding the Limit of Given Functions

Find the limit of the following functions <!--[if !supportLists]-->- <!--[endif]-->Lim ( x --> 0) of [8(x^3+6)/(-4(456)(x^3+6))] <!--[if !supportLists]-->- <!--[endif]-->Lim ( x --> 5) of [10(x-4)(3x-3)/(2x(3x-3))]

Green's function using Laplace

I would like help with the step's to solve the system, I have three parts: x' + x = f(t) using Green's function Given for the force f(t) = ?(t) with the initial condition x(t = 0) = 0. (a) Using the method of Laplace transformation, determine G(s). (b) Determine G(t). (c) Using the Greenâ??s function G(t), determine t

Determining parabola/axis interaction points

#1 A parabola is given by the equation: f (x) =-x^2 + 4x + 5 a) Determine the parabola intersection point with the first axis b) Determine the area of the area bounded by the parabola and the first axis #2 The function f (x) and g (x) is given by: f (x) =-x^3 + 1.5x^2 + 6x - 1 and g (x) = 6.5 - x a) Solve th

Cost Functions: Average, Marginal, and Minimal Average Costs

Please refer to the attached file. For the given cost function C(x)=40000+500x+x2 (the function is 40,000 +500x+x^2) find: a) The cost at the production level 1850 b) The average cost at the production level 1850 c) The marginal cost at the production level 1850 d) The production level that will minimize the average

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