Question: Suppose that is a twice-differentiable function of r, that r = x 2 + y 2 + z 2 , and that Show that

Suppose that ƒ is a twice-differentiable function of r, that r = √x2 + y2 + z2, and thatfxx + fyy + fz = 0.


Show that for some constants a and b,image

fxx + fyy + fz = 0.

Step by Step Solution

★★★★★

3.53 Rating (163 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

To show that r can be expressed as a linear combination of 1r and a constant term we can u... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

Q:

Suppose that is a compact subset of R. If for every x E there exist a nonnegative function f = fx and an r = r(x) > 0 such that f is C on R, f(t) = 1 for t (x - r, x + r), and f(t) = 0 for t (x -...

Q:

If t is a twice differentiable function and f (x) xg(x 2 ), find f'' in terms of g, g', and g''.

Q:

Alejandro Puron recently encountered a dilemma in working with his quality circle (QC) team. One of the team members claims that the QC must always be unanimous in its recommendations....

Q:

Determine the derivative of the function y = arcsin 1+x2 at x = 2. 1. Show that d arcsin* + v1 -x2 = arcsinc. 2. Calculate the derivative of y = arctan ver at x = 0. 3. Calculate the derivative of...

Q:

Problem 8.1. For this problem, f(t) = t 1, g(t) = t 1 and h(t) = |t|. (a) Compute the multipart rules for h(f(t)) and h(g(t)) and sketch their graphs. (b) Compute the multipart rules for f(h(t)) and...

Q:

Consider the following function f : IR - R defined in terms of two continuous functions a : [0, co) - R and b : (-0o, 0) - R: a(x) for x 2 0 f( z) = b(I) for r Equation A . A- I BIUSX x Styles Font...

Q:

. Answer the following questions. 1. (3 points) In Metropolis only taxicabs and privately owned automobiles are allowed to use the highway betwem the airport and downtown. The market for taxi cab...

Q:

please do the following problems and show the work 93. Suppose we know the derivative of a function f is flies} = 1What is the general shape of the graph of f? The Second Derivative Test Denition 45...

Q:

Please help me with the following questions by explaining each. The answers has been identified. I wanted to have a better understanding of these question. I am not intended to cheat or copy and...

Q:

Please help me with the following questions by explaining each. The answers has been identified. Explanatio 16 Required information 3.12/3.12 NOTE: This is a multi-part question. Once an answer is...

Q:

During this course, there will be news about an organization needing to reduce the workforce by thousands of employees. What are the options? What are the advantages and disadvantages of each option?

Q:

Raleigh Couriers is analyzing the possible acquisition of Harwich Restaurants. Neither company has debt. The purchase would increase Releigh's after-tax cash flow by $425,000 every year. The current...

Q:

The _ _ _ _ option must be used when running a program in order to see the results of assert statements. a . - ea b . - debug c . - assert d . - db

Q:

=+b. Construct a boxplot, and comment on the important features of the plot.

Q:

Explain how to set up a surface integral given that you will project the surface onto the xz-plane.

Q:

In Exercises 38, find a piecewise smooth parametrization of the path C. (There is more than one correct answer.) 4 3 2 - y C 1 (2,4) |y=x 2 3 4 X

Q:

In Exercises 58, evaluate S (x - 2y + z) dS. S: z = 15 - 2x + 3y, 0 x 2, 0 y 4

Q:

In a draft transaction, the drawee is the party who ________. a. pays the money stated in a draft b. writes an order for a draft c. demands the draft d. receives the money from a draft

Q:

ased mediate: Decision on whether to launch a nev on the Flxed costs are EPO0O per week uct. A compary is currently manufacturing at on of fuil practical capacity in each of its two prodi 180 There...

Q:

Monkey Mortgage Inc. engaged in the following non - strategic investment transactions during 2 0 2 3 , all with intent to hold to maturity: Required: Prepare an amortization schedule for the Jaguar...