QUESTION 6 [5 marks] (a) Given the equation ytanz + xy + xyz = 3, prove...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
QUESTION 6 [5 marks] (a) Given the equation ytanz + xy + xyz = 3, prove that z is a differentiable function h(x, y) in the neighborhood of the point (x, y, z)=(3, 1.0). Do not forget to show that the point is on the surface. (b) Consider the system of equations: y tanz + xy + xyz = 3 xy + y² +2¹=4 (P) (Q) 2 Prove by using (a) and by considering equation (Q) that z is a differentiable function of in the neighborhood of the point (x, y, z)=(3,1,0). Hint: Start by substituting z=h(x,y) in equation (Q). QUESTION 6 [5 marks] (a) Given the equation ytanz + xy + xyz = 3, prove that z is a differentiable function h(x, y) in the neighborhood of the point (x, y, z)=(3, 1.0). Do not forget to show that the point is on the surface. (b) Consider the system of equations: y tanz + xy + xyz = 3 xy + y² +2¹=4 (P) (Q) 2 Prove by using (a) and by considering equation (Q) that z is a differentiable function of in the neighborhood of the point (x, y, z)=(3,1,0). Hint: Start by substituting z=h(x,y) in equation (Q).
Expert Answer:
Answer rating: 100% (QA)
Sufficient condition for differentiability function q x continuous are a... View the full answer
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
A carbon-fiber-reinforced-plastic composite material contains 64 percent by volume of carbon fibers and is stressed under isostrain conditions. The carbon fibers have a tensile modulus of elasticity...
-
Assume that labor is the only variable input. If a firm's short-run marginal cost is increasing as output rises, which of the following must be true? (A) Average product of labor is constant. (B)...
-
One group of observations or one sample test Suppose we wish to compare the mean dietary intake of a particular group of individuals with the recommended daily energy intake of 7846 kJ per day. The...
-
F udy A big part of communication is sharing personal information with another person. Some information we believe we have the right to be our own and should remain private. However, the degree to...
-
In order to study any possible relationship between expense and return, the following data give percentage of expense ratio and total one-year return for randomly selected stock mutual funds for the...
-
On a multiple-choice exam with 100 questions and 4 possible answers for each question, you get a score of X = 32. Is your score significantly better than would be expected by chance (by simply...
-
A \(0.50-\mathrm{kg}\) wood block initially traveling at \(1.0 \mathrm{~m} / \mathrm{s}\) slides \(0.50 \mathrm{~m}\) on a horizontal floor before coming to rest. What is the average rate at which...
-
Table contains data for the installation of new equipment in a manufacturing process at your customers plant. Your company is responsible for the project. Indirect costs are $10,000 per week, and a...
-
A taxpayer receives two interest payments during the year. One is for $500 from a savings account and is reported in their name. The other payment is for $2,000 and belongs technically to someone...
-
Irreversible first-order reaction in a continuous reactor, a well-stirred reactor of volume V is initially completely filled with a solution of solute A in a solvent S at concentration C AO . At time...
-
RoundRock, Inc. is a qualifying 501(c)(3) organization. Determine if RoundRock, Inc. is a public charity or a private foundation if RoundRock receives its support from the following sources: Grants...
-
A material breach of contract does not discharge the other partys duty to perform. (True/False)
-
Jenny sells her Value Auto Parts store to Burt and makes a valid contract not to compete. Burt wants to sell the store to Discount Auto Centers and assign to Discount the right to Jennys promise not...
-
Under the parol evidence rule, virtually any evidence is admissible to prove or disprove the terms of a contract. (True/False)
-
What are the two principal types of damages recoverable on a breach of contract?
-
Hans owes Bell Credit Company $10,000. Chris orally promises Bell that he will pay Hanss debt if Hans does not. This promise is a. not enforceable because it is not in writing. b. enforceable under...
-
A person with high EQ would be expected to Oquickly become a millionaire never get angry have a zero balance in the emotional bank account Oget along well with other people
-
Provide examples of a situations in which environmental disruptions affected consumer attitudes and buying behaviors.
-
Find y" if x6 + y6 = 1.
-
Use series to evaluate the limit. (a). (b). x In(1 x) lim sin x-x+ lim
-
State the derivative of each function. (a) y = xn (b) y = ex (c) y = ax (d) y = In x (e) y = loga x (f) y = sin x (g) y = cos x (h) y = tan x (i) y = csc x (j) y = sec x (k) y = cot x (l) y = sin-1 x...
-
Describe the link between the size of an organization and the formalization process.
-
Identify and describe the major features of the Strategic Management model.
-
Identify and describe the meaning of the term's formalization and informal.
Study smarter with the SolutionInn App