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Calculus and Analysis

Existence and uniqueness theorem

The existence and uniqueness theorem for ordinary differential equations (ODE) says that the solution of a 1st order ODE with given initial value exists and is unique. It is discussed briefly on p. 528 of the text.<<< this just talks about the ability for a differential eqn. to have practical importance in predicting future valu

Differential equations by systematic elimination

I could use your assistance with a problem. The problem is to be soulved by using MATLAB. I have the stu version 6.0. I'm not real familure with using it, if you could show me the code on the problem I would greatly appriciate it. I have tried for a long time with no headway. I'm sorry, I wrote the problem in complete. t

Calculus II problem

Hi, these three problems are from Calculus II. (See attached file for full problem description)

Region R bounded by the given curves is revolved

(See attached file for full problem description) --- Find the volume of the solid generated when the region R bounded by the given curves is revolved about the indicated axis. Do this by performing the following steps A sketch the region R B show a typical slice properly labeled C write a formula for the approximate vo

Monte Carlo

What fraction of the area of a square is closer to the center of the square than to any edge of the square? This one is harder than it looks! I am looking for an exact answer, but you can get a rough numerical estimate by a Monte Carlo method , and this might help you check your answer. I have no idea where to begin this prob

Mean Value Theorem

(See attached file for full problem description with proper symbols and equations) --- First: solve these problems. Second: check my answers. Third: if my answers are wrong explain why. Let . Explain whether or not the Mean Value Theorem applies on the interval [1,8]. If it does, find the number c that is guarant

Need only answers

I need only the answers with short explanation to the attached questions. I just need to check my answers and correct myself where i have gone wrong.

Newtons Method Using Mathematica 5

If its possible to answer these three questions using mathematica 5 if matlab looks similar, or the commands are similar then i guess matlab is fine... if its at all possible for mathetmatica it would be much appreciated Using Newtons Method 1. Plot f(x) = a on the interval - 3 &#8804; x &#8804; 3. a) Use Newton


The function is f(x) = 5x^2 / (x^2 + 2) I need to find the x and y intercepts all asymptotes and inflection points. I know only how to do this if I have a closed interval if you could walk me through this step by step use the critical number and f'(x) and f''(x) graph

Finding a set of points and a 1-1 function

(See attached file for full problem description with equations) --- Let . (a) Find the set of points at which . (b) Let . Find a set V such that f takes U onto V in a one-to- one fashion and the inverse function g on V. ---


File is attached. I need only the answers with work shown in very shortly. I just need to check my answers.

Differential Equations of Exponential Functions

Differential Equation (IX): Formation of Differential Equations by Elimination Eliminate the arbitrary constants from the equation: y = Ae^x + Be^2x + Ce^3x. Make sure to show all of the steps which are involved.

Differential Equations : Solutions, Electric Circuit and Step Function

Find the general solution of each of the differential equation y ''- y ' = x2 . If the solution is not valid over the entire real axis, describe an interval over which it is valid. If k is a nonzero constant, prove that the equation y ''+ k2y = R(x) has a particular solution 1 y given by ..... Find the general solution of

Solve the differential equation.

The presence of toxins in a certain medium destroys a strain of bacteria at a rate jointly proportional to the number of bacteria present and to the amount of toxin. If there were no toxins present, the bacteria would grow at a rate proportional to the amount present. Let x denote the number of living bacteria present at time t.

Evaluate the Limit

Please explain how to evaluate the limit lim/k arrow to 0 f(x = h) - f(x)/h using the rules for finding the derivative of f.

Differential Equation - Initial Value Problem

11. Consider an electric circuit like that in Example 5 of Section 8.6. Assume the electromotive force is an alternating current generator which produces a voltage V(t) = E sinwt , where E and w are positive constants (w is the Greek letter omega). EXAMPLE 5. Electric Circuits. Figure 8.2(a), page 318, shows an electric circu