Let S be the cylinder defined by x + y = 4 and 2 ...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Let S be the cylinder defined by x² + y² = 4 and −2 ≤ ≈ ≤ 2. (a) Note that as = C₁ C₂ where C₁ (resp. C₂) is the circle at the top (resp. bottom) of the cylinder. Give parametrizations c₁ and c2 of C₁ and C2₂ with the orientation corresponding to outwards pointing normal vectors for S. (b) Use part (a) and Stokes' theorem to evaluate 1₂0 (V x F). dS for F(x, y, z) = x²i+y²j+xye²k. Here S is oriented with outwards pointing normal vectors. Let W be the top half of the ball of radius R> 0 centered at (0, 0, 0), i.e., the surface given by x² + y² + z² ≤ R² and z ≥ 0. (a) Describe W as an elementary region in R³. (b) Use part (a) and Gauss' divergence theorem to evaluate How F.dS, where F(x, y, z) = (x³ + eª, y³ − z, xy + z³) and OW is oriented with outwards pointing normal vectors. 7 Let S be the cylinder defined by x² + y² = 4 and −2 ≤ ≈ ≤ 2. (a) Note that as = C₁ C₂ where C₁ (resp. C₂) is the circle at the top (resp. bottom) of the cylinder. Give parametrizations c₁ and c2 of C₁ and C2₂ with the orientation corresponding to outwards pointing normal vectors for S. (b) Use part (a) and Stokes' theorem to evaluate 1₂0 (V x F). dS for F(x, y, z) = x²i+y²j+xye²k. Here S is oriented with outwards pointing normal vectors. Let W be the top half of the ball of radius R> 0 centered at (0, 0, 0), i.e., the surface given by x² + y² + z² ≤ R² and z ≥ 0. (a) Describe W as an elementary region in R³. (b) Use part (a) and Gauss' divergence theorem to evaluate How F.dS, where F(x, y, z) = (x³ + eª, y³ − z, xy + z³) and OW is oriented with outwards pointing normal vectors. 7
Expert Answer:
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
Students also viewed these mathematics questions
-
Let S be the surface of the cylinder (not including the top and bottom) of radius 2 for 1 z 6, oriented with outward-pointing normal (Figure 16). (a) Indicate with an arrow the orientation of S...
-
Let S be the side of the cylinder x2 + y2 = 4, 0 z 2 (not including the top and bottom of the cylinder). Use Stokes' Theorem to compute the flux of F = (0, y,z) through S (with outward pointing...
-
1). The gross earnings for the pay period are: (LO1, 2, 3) a). $1,400.00 b). $1,490.00 c). $1,582.31 d). $1,682.31 2). Pensionable earnings are: (LO1, 2, 3) a). $1,490.00 b). $1,698.46 c). $1,598.46...
-
In FIGURE CP12.88, a 200 g toy car is placed on a narrow 60-cm-diameter track with wheel grooves that keep the car going in a circle. The 1.0 kg track is free to turn on a frictionless, vertical...
-
A soap bubble of radius r is inflated with an ideal gas. The atmospheric pressure is Po, the surface tension of the soap water solution is a. Find the difference between the molar heat capacity of...
-
A diffraction experiment involving two thin parallel slits yields the pattern of closely spaced bright and dark fringes shown in Fig. 36.33. Only the central portion of the pattern is shown in the...
-
The following MINITAB output presents a confidence interval for a mean response and a prediction interval for an individual response. a. Predict the value of y when x1 = 1.32, x2 = 1.58, and x3 =...
-
Jordans Furniture is a unique retail chain. In fact, every one of its stores in New England is uniqueand highly profitable. And thats what caught the eye of Warren Buffett, the head of conglomerate...
-
Problem 5. Efficient Frontier and the CAPM. Short answer questions. 1. Explain why the efficient frontier must be concave. 2. Suppose that there are N risky assets in an economy, each being the...
-
The director of RCM inc. plans to launch a new product. The initial investment in equipment and other fittings is $800,000. It's been a while since management thinking of launching this new product....
-
How do keystone species influence the stability and resilience of ecosystems, particularly in the context of trophic cascades?
-
Israel Company provided the following facts regarding pending litigation at year-end: Lawsuit 1: Israel is defending against a lawsuit and believes there is only a 40% chance it will loss in court....
-
Santana Rey has consulted with her local banker and is considering financing an expansion of her business by obtaining a long-term bank loan. Selected account balances at March 31, 2022, for Business...
-
Identify the five most important privacy issues which Amazon company must address as part of its enterprise risk management program. Focus on strategic issues, e.g. lack of management support, lack...
-
Analyze the concept of "the unreliable narrator" in modern literature. What techniques do authors use to create ambiguity, and how does this affect the interpretation of the narrative ?
-
Discuss the significance of the "stream of consciousness" technique in literature. What does this approach reveal about character psychology, and how does it alter the traditional linear progression...
-
Billie hurried into a local department store just before closing time when all the clerks werenclearing their registers and flickering the lights to signal customers it was time to go. It was...
-
For the following exercises, find the inverse of the function and graph both the function and its inverse. f(x) = 4 x 2 , x 0
-
In June of 2012, Maureen's house is vandalized during a long-term power failure after a hurricane hit the city. The president of the United States declares Maureen's city a disaster area as a result...
-
Fisafolia Corporation has gross income from operations of $220,000 and operating expenses of $160,000 for 2012. The corporation also has $20,000 in dividends from publicly traded domestic...
-
In 2012, Michael has net short-term capital losses of $2,000, a net long-term capital loss of $45,000, and other ordinary taxable income of $45,000. a. Calculate the amount of Michael's deduction for...
-
Prove that \(C_{P}-C_{V}=\frac{T V \beta^{2}}{\alpha}\) where \[ \alpha=\text { Isothermal compressibility } \] \[ \begin{equation*} \beta=\text { Volume expansivity } \tag{WBUT,2007} \end{equation*}...
-
Prove that \[ d H=C_{P} d T+\left[V-T\left(\frac{\partial V}{\partial T} ight)_{P} ight] d P \]
-
Show that \(\left(\frac{\partial U}{\partial P} ight)_{T}=(\alpha P-\beta T) V\).
Study smarter with the SolutionInn App