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
For the following graph the given functions on a computer screen, how are these graphs related? 1) Y=2^x, y=e^x, y=5^x, y=20^x 2) Y=3^x, y=10^x, y=(1/3)^x, y=(1/10)^x _______________________________________________________________________ Make a sketch of the function. 7) y=4^x-3 8) y=-2x^-x 9) y=3-e^x 13)
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
Please show the steps necessary to solve: ∫ dx ∕ (x - 2 )√(x² - 4x + 3)
Differential Equations : Show that the differential equation ... is not exact. Make exact and solve.
Show that the differential equation is not exact. It can be made exact by multiplying throughout by , where m and n are integers. Find m and n and hence, or otherwise, solve the equation. Please see the attached file for the fully formatted problems.
Differential Equations : Solve the following differential equation by as many different methods as you can.
A) Solve the following differential equation by as many different methods as you can. (See attachment for equation) b) There is a type of differential equation which will always be solvable by two different methods. What type of differential equation is it and which other method can always be used to solve it? ---
1. Please see the attached file for the fully formatted problems. a) Use separation of variables to solve b) Solve the following exact differential equation c) By means of substitution y=vx solve the differential equation d) By means of the substitution for approipriate values of and , solve the d
Functions and Rate of Change : Find the rate of change of the function f(x) = 2x - 9 over the interval x=-1 to x=12.
Find the rate of change of the function f(x) = 2x - 9 over the interval x=-1 to x=12.
2. Use any method for xy'=2y-3x
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
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
Could someone please help me with the problem and show me all the steps? (See attached file for full problem description). dy/dx - (xy + 2y - x - 2)/(xy - 3y + x - 3)
Find the Hessian. See attached file for full problem description.
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
Solve the Initial Value Problem y'' + 4y' + 5y = 35e^(-4x) given: y(0) = -3, y' (0) = 1
LaPlace Transform : Solve y'' + y = Sqrt2Sin(t Sqrt2), with y(0) = 10 and y' (0) = 0 using the method of the LaPlace Transform.
Solve y'' + y = Sqrt2Sin(t Sqrt2), with y(0) = 10 and y' (0) = 0 using the method of the LaPlace Transform.
Fundamental set of solutions of a Differential Equation : Verify that e^x Cos(2x) and e^x Sin(2x) form a fundamental set of solutions of the differential equation [ y'' - 2y + 5y = 0 ] on the ...
Verify that e^x Cos(2x) and e^x Sin(2x) form a fundamental set of solutions of the differential equation [ y'' - 2y + 5y = 0 ] on the interval (- infinity, infinity). With the e^x the "x" is the only upper score in the problem. The Cos and Sin are on the regular line of the problem.
General Solution of the Higher-Order Differential Equation : 16 d^(4) y / dx^(4) + 24 d^(2) y / dx^(2) + 9y = 0
Could you provide assistance on setting up and working of the problem. 16 d^(4) y / dx^(4) + 24 d^(2) y / dx^(2) + 9y = 0
Fundamental Set of Differential Equations on an Indicated Interval : y'' - y' - 12y = 0; e^-3x, e^4x, (-∞, ∞ )
Y'' - y' - 12y = 0; e^-3x, e^4x, (-∞, ∞ ) Could you provide assistance on setting up and working of the problem.
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
ODE - Lagrange's Equation : y=x(1+y')+(y')^2
Bernoulli Differential Equation : y''-(3/(2y))*((y')^2)-2*y =0
Find the function "f(x)" which this sum converges to on the I.O.C.. ∞ Σ ((n+1)x^n)/(2^n) n= 0
Hi, these three problems are from Calculus II. (See attached file for full problem description)
(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
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
(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
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.
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 ≤ x ≤ 3. a) Use Newton