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Calculus and Analysis

Brief Calculus

Please answer the following questions: The Present value of money is the amount that you need to deposit now in order to have a desired amount sometime in the future . 1. What is the present value needed in order to have saved $60,000 in five years, given an annual interest rate of 7% compounded monthly? 2. What is the

Identities

Prove the given identity - Please explain in detail. 14. 2 cos x - 2 cos^3x = sin x sin 2x 16. cos (x-y)/cos x cosy = 1 tan x tany 20. sec x -cos x = sin x tanx 22. sin 2x = 1/tanx +cot 2x 23. If tan x = 5/12 and sin x>0 , find sin 2x 26. If sin x = -12/13 with pie <x<3pie/2, and sec y = 13/12 with 3 pi

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: &#8747; dx &#8725; (x - 2 )&#8730;(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