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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


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 use Mathematica, Maple or Ma

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?

Find formula for sequence

Hi, I need to find a formula for the sequence below by first finding a recurrence for a_n, then solving the recurrence. Thanks! a_n = 1/2 + 2/4 + 3/8 + 4/16 + 5/32 + · · · + n/(2^n) = sum_{k=1}^n (k /(2^k))


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

Calculus Problems

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(

Business calculus

1. Sketch Graph: f(x) = 3x4-2x³-12x²+18x (MUST SHOW ALL WORK) 2. Sketch Graph: f(x) = x4-18x²+81 (MUST SHOW ALL WORK) Note: The 4 in both problems is an exponent

Questions on rectilinear motion in basic mechanics

I need help doing two calculus problems #11, and #13. Each one is 5 parts (a,b,c,d,e) I have attached 3 files a) class notes for rectilinear motion b) the assignment (only problems 11 and 13) and my initial work on #11. I understand how to calculate 11 a, b, c but I get stuck on d, e. Can you explain what is going on and d

Proof of a property of Wronskian for a given differential equation.

Suppose that y1, y2 are linearly independent solutions to the differential equation: a2 (x) y'' + a1 (x) y' + a0 (x) y = 0. a) Show that a2 (y1 y2'' - y2 y1'') + a1(y1 y2' - y1' y2) = 0 b) show that (a) implies a2 W' + a1 W = 0 {here W means the Wronskian) c) show that the equation in (b) implies W

Sequences and Binomial Expansions

3. Write the first four terms of the defined sequence a lower case 1 = 1 a lower case n=na lower case n-1, n>1 9. Write the following in summation notation 3+6+9+12+15 10. Write the following in summation notation: x+x^2/2 + x^3/6 + x^4/24 14. Find the fifth term in the expansion of (a + b)^16 15. Write the bi

Frobenius Method

Use a power series method to find the solution of x^2 y'' + 2xy' + 4y = 0 that is valid in any interval not including the singular point. y=0 is a trivial solution which exists for any linear Homogeneous equation. So it is correct but absolutely not enough to complete the problem. Since the equation is linear and has non

Solving a differential equation with initial condition.

A relation between a function f(x) and its derivative f'(x) = x√f(x) is given with an initial condition on f(x) as f(4)=16. One needs to find the value of the second derivative of the function i.e., f"(4). Also an expression to f(x) in terms of x is to be evaluated. Please see the attached file for the fully formatted

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

Convergence Tests

Does the series a_n defined by the formula below converge or diverge? Give reason for your answer. a_1 =3 a_(n+1) =( n / n + 1)(a_n)

Applications of integration

Let f and g be the functions given by f(x) = ¼ + sin(Pi*x) and g(x) = 4^ -x. Let R be the shaded region in the first quadrant enclosed by the y-axis and the graphs of f and g, and let S be the shaded region in the first quadrant enclosed by the graphs of f and g. a) Find the area of R. b) Find the areas of S. c) Find t