Let G(x, y, z)= (1+9xy)? and consider a surface S given by the parametrization rlu, v)=[u, u", v], 0sus1,0svs2.Then the value of the surface integral | G(r)dA is given byOA 14O B. 146.Ос. 28O D. None of theseConsider the surface integral of the vector field F [xy, 3x, x²z]over a surface S,where S consists of the cylinderx? + y? =9, 0szs2, and two discs x2+ y? <9, z=0 and x² +y? s9, z=2. If we apply Gaussian divergence theorem, thenthe value of this surface integral will beO A. 81 7ОВ. 81п2.OC. BIO D. None of these5一9

Since you have asked multiple question, we will solve the first question for you. If you want any…

Let G(x, y, z)= (1+9xy)? and consider a surface S given by the parametrization rlu, v)=[u, u", v], 0su31,0svs2. Then the value of the surface integral G(r)dA is given by OA 14 ОВ. 14 6. Ос. 28 5. O D. None of these 5一9

Let G(x, y, z)= (1+9xy)? and consider a surface S given by the parametrization rlu, v)=[u, u", v], 0su31,0svs2. Then the value of the surface integral G(r)dA is given by OA 14 ОВ. 14 6. Ос. 28 5. O D. None of these 5一9

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: 5. Consider the surface: x(u, v) y(u, v) z(u, v) where u € [0, 1] and v € [0,2]. Calculate the area…

A: Introduction: The area is the area occupied by a two-dimensional flat surface. It has a square unit…

Q: Evaluate the line integral / Vxy° +3 dx +6xy" dy, where C any curve joining (1, -1) to (16, 1).

Q: 03. The equation of the tangent plane to the surface f(x,y) at the point (1,1) is 2x + 2y = 9, find:…

A: We have given equation of tangent plane 2x+2y=9which is incorrect because left side is even number…

Q: Let F= (0,0, z) and S be the part of the paraboloid z = x² + y² between the plan z = 1 and 2 = 4,…

Q: 3. let F= Kxyz, xy, xfuz> where $ consists of the top 5, and the four Dides (mot the bottom) of the…

A: Given- Let F→ = xyz, xy, x2yz. To find- Use Stokes's Theorem to evaluate ∬Scurl F→·dS where S…

Q: Assume S is the surface x1000+y8000+z1000 = 10¹2 and f = (9+ eyz, x³yz, 3x - 5y - 6 cos(zx)).…

A: Here we use the Divergence theorem for a surface S inclosing a volume V

Q: Find Əz ?х Əz da Əz ду = ab brackets (e.g. x*y rather than xy; 2*(x+y) rather than 2(x+y)). • Put…

Q: x² + y³. 2 = Consider the surface S of equation (1, 1, v), An equation for the tangent line tangent…

A: We have to find the equation of tangent line.

Q: QUESTION 6 Use the Green's Theorem to evaluate the line integral xfydx +xy dy. where C is the…

A: Using the given vertices we can draw the required triangle and then apply Green's theorem to…

Q: F. dr Evaluate So

A: In this question, we have to evaluate the line integral for given vector function along the given…

Q: Determine the surface area of the plane 2x+y + 2z = 16 cut off by x = 0, y = 0 and x² + y² = 64.

A: Area of surface given by z = f(x,y) A=∫∫Dfx2+fy2+1dA where (x,y) is a point from the region D in…

Q: Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x²…

A: Solution: If surface 's' has equation of form z= f(x,y) and if 'f' has continous partial…

Q: 1. Let F(x, y,z) = (x + y², y + z²,z + x²). Let C be the triangle with vertices (1,0,0), (0,1,0),…

A: Consider the provided question,

Q: 10. Find all the planar and hyperbolic points on the surface o(u, v) = u-3uv².

A: A point on a surface is said to be a hyperbolic point if the Gaussian curvature at p,i.e., κp<0.…

Q: Compute the line integral -xdy + ydx 2(x-y)2 +4xy where L is the circle (1-x)2 + y2 = 3 with a…

A: We can write the given line integral as ∫L y2x-y2+4xydx+-x2x-y2+4xydy, where L is the circle…

Q: 5. Let L₁ be the line with parametric form (x, y, z) = (1, 0, 2) + (-1,2,3), and let L₂ be the line…

A: Given,The parametric form of the line ,The parametric form of the line ,.Aim: (a) To find the angle…

Q: Let l be the line and let S be the surface x = 4+2t, y = 3 +t, z = 8-2t, z = xy + e*. Find the…

A: Giventhe equation of line the equation of curve is given as to find the equation of plane that is…

Q: 4. Find both points on the surface xz – x2 – y? = 8 where the tangent plane is horizontal.

Q: (2u cos v, 3u sin v, u²) and find tangent plane at Describe/Sketch the surface given by r = (0,6,4)

A: Given, To find: equation of tangent plane ate (0,6,4)

Q: Find y'(0) and y"(0) from the following table ofvalues: X 0 1 2 y 4 8 15 3 4 7 6 5 2

A: From the given table upper digits are values of X and lower digits are values of Y(X).

Q: Find the equation for the tangent plane to the surface z = 6x² - 8y² at the point (2, 1, 16). OA.…

A: NOTE: Refresh your page if you can't see any equations. . so the function f is, the given point…

Q: Consider the function (a) Find z = 3e- cos x + 2e* siny. 8²% Әхду 8²z дудх -(0,0) -(0,0) and (b)…

A: Function: z=3e-ycos x+2exsin y To find: a) ∂2z∂x∂y0,0 and ∂2z∂y∂x0,0 b) The slope of the surface…

Q: 5. If X any Y are sets, then X-Y= {r€ X: 1¢Y} If X is open set and Y is closed set. Prove that (a)…

Q: Which of the following is the tangent plane to z = 2x² + y² at the point (1, 1, 3)? z = 4x + 2y z =…

Q: Find an equation of the plane tangent to the following surface at the given points. z=ln(1+xy);…

Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

A: We have to use Langrages Multipliers Method to find the minimum distance from (0,c,0) to a point on…

Q: Find the length of the curve y =Vx³, for [0, 4]. Find also the surface area of the region is rotated…

Q: Find an equation of the tangent plane to the surface given implicitly by z= sin(zy) at the point (,…

A: A tangent plane to a surface is a plane that just touches the surface at a single point. The…

Question

Let G(x, y, z)= (1+9xy)? and consider a surface S given by the parametrization rlu, v)=[u, u", v], 0sus1,0svs2.
Then the value of the surface integral | G(r)dA is given by
OA 14
O B. 14
6.
Ос. 28
O D. None of these
Consider the surface integral of the vector field F [xy, 3x, x²z]over a surface S,where S consists of the cylinder
x? + y? =9, 0szs2, and two discs x2+ y? <9, z=0 and x² +y? s9, z=2. If we apply Gaussian divergence theorem, then
the value of this surface integral will be
O A. 81 7
ОВ. 81п
2.
OC. BI
O D. None of these
5一9

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step by step

Solved in 5 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Triple Integral$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

PLz don't take the answer of any other expert if u take i will give u thumb down so do by yourself
What geometric transformation of 3D space happens in this matrix-vector multiplication? 010 -1 0 0 0 01 9).( (3) Please note: All rotation directions to be understood as when looking along the rotation axis towards the origin. O Clockwise rotation by 90 degrees around the x3 axis Counter-clockwise rotation by 90 degrees around the x3 axis Clockwise rotation by 90 degrees around the x₂ axis Counter-clockwise rotation by 90 degrees around the x2 axis O Clockwise rotation by 90 degrees around the x₁ axis Counter-clockwise rotation by 90 degrees around the x₁ axis O Mirroring across the x₁-x2 plane Mirroring across the x₁-x3 plane Mirroring across the X₂-X3 plane
8) Answer the question shown in the image
8) Answer the question shown in the image
Answer it as soon as possible
Find the matrix of the linear transformation T from R? R?, where T([1, 0]) = [1, -2], and T([2, 1]) = [2, 3] (Note: matrix A = [T([1,0]), T([0, 1])] ). 1 (a) 1 (b) 1. (c) -2 1 -2 3 -2 1 (d) 0. 3
Solve in 10 min plz
4. Find дw b. dz a. дх at the point (x, y, z) = (0, 1, T) if w = x² + y? + z? and y sin z + z sin x = 0.
3. Consider the surface sin (xy)+ cos (xz)+ sin ( yz) =1. Find an equation for the tangent plane to the surface at the point (7,1,0).
Q.2 Find curlF at point (1,0,0) where f(x, y, z) = xe*y + y +
Let T : R2 → R² be the linear transformation which rotates vectors counter-clockwise about the origin by 7T/3 radians (60 degrees). (i) Find the standard matrix of the linear transformation T. (ii) Use your matrix to rotate the vector v = counterclockwise about the origin by 4 T/3 radians.
13) The integer n = a) If n = 3 (mod 9), then what is x ? b) If n = 3 (mod 11), then what is x ? Hint for #13: 12700140x3243243 is missing the digit x. Consider the number 1234. By writing each digit in scientific notation, we have 1234 1 x 10³ +2× 10² +3 × 10¹ + 4 × 10⁰ Then notice that 10 = 1 (mod 9). When we reduce mod 9, we obtain 1234 1 x 10³ +2× 10² +3 x 10¹ + 4 x 10⁰ = = 1x 1³ + 2 x 1² + 3 × 1¹ + 4 × 1⁰ = 1+ 2+ 3+ 4 = 10 = 1 (mod 9). Since 10 = -1 (mod 11), when we reduce mod 11, we obtain 1234 1 x 10³ +2× 10² +3 x 10¹ + 4 x 10⁰ = = 1x (-1)³ +2× (-1)² +3 × (-1)¹ +4× (-1)⁰ = -1 + 2-3 + 4 = 2 (mod 11).