a- Let P (x, y) and Q (x, y) be continuous and have continuous first partial...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
a- Let P (x, y) and Q (x, y) be continuous and have continuous first partial derivatives at each point of a simply connected region R. A necessary and sufficient condition that [P dx + Q dy] =0 around every closed path C in R is that identically in R. Similiarly we can conclude that a necessary and sufficient condition that [P dx + JP JQ ay əx JP 20 Q dy] be independent of the path in R joining points A and B is that ay ax identically in R. Which theorem can be used to prove these statements? = b- According to the above mentioned statements, prove that √ [(6xy² − y³)dx + (12) (6x²y3x y²) dy is independent of the path joining (1.2) and (3, 4). c- Find the value of Integral by using potential function. a- Let P (x, y) and Q (x, y) be continuous and have continuous first partial derivatives at each point of a simply connected region R. A necessary and sufficient condition that [P dx + Q dy] =0 around every closed path C in R is that identically in R. Similiarly we can conclude that a necessary and sufficient condition that [P dx + JP JQ ay əx JP 20 Q dy] be independent of the path in R joining points A and B is that ay ax identically in R. Which theorem can be used to prove these statements? = b- According to the above mentioned statements, prove that √ [(6xy² − y³)dx + (12) (6x²y3x y²) dy is independent of the path joining (1.2) and (3, 4). c- Find the value of Integral by using potential function.
Expert Answer:
Related Book For
Probability And Statistics
ISBN: 9780321500465
4th Edition
Authors: Morris H. DeGroot, Mark J. Schervish
Posted Date:
Students also viewed these accounting questions
-
(a) Show that the curvature at each point of a straight line is k = 0. (b) Show that the curvature at each point of a circle of radius is k = 1/r.
-
Sketch the graph of f (x). At each point of discontinuity, state whether f is left- or right continuous. 51. 53. for x < 1 1 xfor1 f(x) =1 x- 2-x for x > f(x) = -3x + 2 |x-21 f(x) = f(x) = |
-
1 2 D 3 4 MRP assignment 4.1 5 Lot-for-lot Model 6 7 Week Number 8 9 Item A: LT= 1 week 10 Gross Requirements 11 Scheduled Receipts 12 Projected on Hand 13 Net Requirements 14 Planned-Order Receipts...
-
A charged isolated metal sphere of diameter 10 cm has a potential of 8000 V relative to V = 0 at infinity. Calculate the energy density in the electric field near the surface of the sphere.
-
Property, plant and Equipment (plant assets) generally represent a material portion of the total assets of most companies. Accounting for the acquisition and usage of such assets is therefore an...
-
The following transactions of Beltville College transpired during 2025. The funds necessary are the Endowment Fund, the Annuity Fund, the Plant Fund Unexpended, the Plant Fund Investment in Plant,...
-
Classify the fluids based on their properties.
-
Salvania Corporation is considering investing in Farnorth Corporation, but is unsure about what level of ownership should be undertaken. Salvania and Farnorth have the following reported incomes:...
-
i need help with this question with an explanation thanks! 7) Large Co. pays its employees $20,000 gross salary each week. 30% of salary is withheld for income taxes and 5% is withheld to pay Social...
-
The following cross tabulation shows the average speed of the 25 winners by year of the Daytona 500 automobile race (The 2013 World Almanac). a. Calculate the row percentages. b. W hat is the...
-
During the year, Silk sold Bruce goods for $16,000, which included a mark-up of one-third. 80% of these goods were still in inventory at the end of the year. Non-controlling interests are measured...
-
In a recent study, the Centers for Disease Control reported that diastolic blood pressures (in \(\mathrm{mmHg}\) ) of adult women in the United States are approximately normally distributed with mean...
-
In what way can we show in UML that something is contained within something else, for example a subsystem within another subsystem?
-
Let \(\mathbf{F}\) be a vector field whose curl and divergence at the origin are \[ \operatorname{curl}(\mathbf{F})(0,0,0)=\langle 2,-1,4angle, \quad \operatorname{div}(\mathbf{F})(0,0,0)=-2 \]...
-
How has health reform legislation affected the organization and management of corporate health institutions?
-
Prove the following tautologies by starting with the left side and finding a series of equivalent wffs that will convert the left side into the right side. You may use any of the equivalencies in the...
-
The data given below are from the accounting records of the Kuhn Corporation: Net Income (accrual basis) Depreciation Experise Decrease in Accounts Payable Decrease in Inventory Increase in Bonds...
-
Q1) What is the a3 Value Q2) What is the a7 Value Q3) What is the a4 Value Q4) What is the b3 Value Q5) What is the b2 Value Q6) What is the sign of 2nd constraint? A pastry chef at a bakery wants to...
-
Assume that X1, . . . , Xn are i.i.d. with the normal distribution that has mean and variance 1. Suppose that we wish to test the hypotheses H0: 0, H1: >0. Consider the test that rejectsH0 if Z ...
-
Suppose that (X1, Y1), . . . , (Xn, Yn) are i.i.d. pairs of random variables with a continuous joint distribution. Let p = Pr(Xi Yi), and suppose that we want to test the hypotheses H0: p 1/2, H1:...
-
Suppose that a random sample of 10 observations X1, . . . , X10 is taken from the normal distribution with unknown mean and unknown variance 2, and it is desired to test the following hypotheses:...
-
A child on a sled slides down an icy slope, starting at a speed of \(2.5 \mathrm{~m} / \mathrm{s}\). The slope makes a \(15^{\circ}\) angle with the horizontal. After sliding \(10 \mathrm{~m}\) down...
-
A particle is accelerated such that its position as a function of time is given by \(\vec{x}=b t^{3} \hat{t}\), with \(b=1.0 \mathrm{~m} / \mathrm{s}^{3}\). What is the particle's acceleration as a...
-
The position of a cart on a low-friction track can be represented by the equation \(x(t)=b+c t+e t^{2}\), where \(b=4.00 \mathrm{~m}, c=6.00 \mathrm{~m} / \mathrm{s}\), and \(e=0.200 \mathrm{~m} /...
Study smarter with the SolutionInn App