If f and g are twice differentiable functions of a single variable, show that the function u(x,

Question:

If f and g are twice differentiable functions of a single variable, show that the function
u(x, t) = f (x + at) + g(x - at)
is a solution of the wave equation given in Exercise 78.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Calculus Early Transcendentals

ISBN: 978-1285741550

8th edition

Authors: James Stewart

See More Books

Question Posted: Apr 10, 2019 08:35 AM

See More Questions

If y = f(u) and u = g(x), where f and are twice differentiable functions, show that d'y ( du dy d'u du dx d'y du? dx
If f and t are twice differentiable functions, show that 2 (fg) = f 2 g + g 2 f + 2f g v(fg) = fVg + gVf + 2Vf Vg
Assume a curve is given by the parametric equations x = f(t) and y = g(t), where f and g are twice differentiable. Use the Chain Rule to show that
Engineering is a dynamic field that requires continuous learning. Discuss how you plan to acquire and apply new knowledge as needed throughout your engineering career. Address the strategies you...
Is the cost of a job related to the price charged? Explain. Discuss.
A program contains three functions named main, calcGross, and displayGross. Two of the functionsmain and calcGrossdeclare a variable named pay. The pay variable name also appears in the displayGross...
Refer to Samsungs financial statements in Appendix A. Compute its debt ratio as of December 31, 2015, and December 31, 2014. Data From Samsung Financial Statement Appendix A Samsung Electronics Co.,...
Fredonia Inc. had a bad year in 2013. For the first time in its history, it operated at a loss. The companys income statement showed the following results from selling 80,000 units of product: net...
The adjusted trial balance for Chiara Company as of December 31 follows. Cash Accounts receivable Interest receivable Debit $ 30,000 Credit 52,000 18,000 nt ok Notes receivable (due in 90 days)...
In this exercise, you create a Triangle class and a program that uses the Triangle class to instantiate a Triangle object. a. If necessary, create a new project named Intermediate17 Project and save...
Show that each of the following functions is a solution of the wave equation u t t = a 2 u xx . (a) u = sin(kx) sin(akt) (b) u = t/(a 2 t 2 - x 2 ) (c) u = (x - at) 6 + (x + at) 6 (d) u = sin(x - at)...
The diffusion equation c/t = D 2 c/x 2 where D is a positive constant, describes the diffusion of heat through a solid, or the concentration of a pollutant at time t at a distance x from the source...
The black modification of SnO is isostructural with PbO litharge of the previous problem. (a) The bond-valence parameters for Sn 2+ O are R 0 = 1.98 and B = 0.37 . Use Equation (5.18) (d ij = R 0 ij...
When George speaks of Liberty, what does he mean? Is it simply equal rights, or is it something else?
Do you employ the appropriate superstructure for this audience and purpose? Does cover letter expand on important. Does each paragraph of your letter have a clear purpose and important content for...
Calculate the buoyant force on 149 kg of solid steel completely submerged in water. Density of steel is 7800 kg/m. Write only the numerical value as your answer. Do not include units.
What does the study "Reexamining english only in the ESL Classroom" by Elsa Auerbach say about langauge barriers for effective teaching ?
What are the reasons consumers may not be interested in sustainable furniture other than the price?
Malbasa Tax Services prepares tax returns for senior citizens. The standard in terms of (direct labor) time spent on each return is 4 hours. The direct labor standard wage rate at the firm is $16.50...
Question 2 For an n x n matrix A = form) via (aij)
Differentiate f and find the domain of f. (a) f(x) = x/ 1 - ln(x - 1) (b) f(x) = ln(x2 - 2x)
Differentiate the function. (a) f(x) = sin (ln x) (b) f(x) = ln 1/x (c) f(x) = log10(x3 + 1)
If f(x) = ln x/ x2, find f'(1).
Ashby, one of Home Depot's suppliers, has a selling price per unit is $12.00, and their variable expense per unit is $7.75, and the break-even sales in dollars is $460,200, what are Ashby's total...
How would investors and creditors know about the change in inventory value?
Assuming an average selling price of $50 per unit, calculate the number of units needed to sell to achieve the survival revenues.

If f and g are twice differentiable functions of a single variable, show that the function u(x,

Question:

Step by Step Answer:

Let v x at wxat Then u aa fv agw t Uz f...View the full answer

Calculus Early Transcendentals

Students also viewed these Mathematics questions