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Calculus and Analysis

Limits and L'Hopital's Rule (34 Problems with High Quality Solutions)

Find the limits using L'Hopital's rule where appropriate. If there is a more elementary method, consider using it. If L'Hospital's rule does not apply explain why. 1) lim as x approaches -1 (x^2 -1) / (x + 1) 2) lim as x approaches -1 (x^9 -1) / (x^5 - 1) 3) lim as x approaches -2 (x+2) / (x^2 +3x + 2) 4) lim as x approa

Inverse functions

Please solve each problem with a detailed solution showing each step to solve the problem. Since the symbols confuse me at times please use "baby" math to show how to get from the start to the end. I understand the book in some ways, but the more I see completed the better I can think about the rest of the problems I need to d

Evaluate the integral

Please show the steps necessary to solve: ∫ dx ∕ (x - 2 )√(x² - 4x + 3)

Cauchy principal value, residue

Verify the integral formula with the aid of residues. 1.) Show that the p.v. of the integral of (x^2+1)/(x^4+1) from 0 to infinite = (pi)/(sqrt 2). Note: p.v.=principal value; pi is approximately 3.14; sqrt 2=square root of 2 Please show all work and explain the steps, especially how you found the zeros of the

LaPlace transformations

Could some one please help me with the problem and provide all the steps. y'' + y = SQRT2 * Sin (tSQRT2) with y(0) = 10 and y' (0) = 0

Find the Hessian

Find the Hessian. See attached file for full problem description.

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