Solve this calclusQuestion 15. 3, x = 0, y = 0.Us över the stated curved surface.15 Evaluate F. dS, where F is the vector field x²i +2zj - yk, over the curvedsurface S defined by x² + y = 25 and bounded by z = 0, z = 6, y 2 3.%3D16. A region V is defined by the quartersphere x2 + y2 + z? = 16, z 2 0, y 2 0 andthe planes z = 0, y = 0. A vector field F = xyi +y²j+k exists throughout andon the boundary of the region. Verify the Gauss divergence theorem for theregion stated.17 A surface consists of parts of the planes x = 0, x = 1, y = 0, y = 2, z = 1 in thefirst octant. If F = yi + x²zj + xyk, verify Stokes' theorem.18 Sis the surface z = x² + y² bounded by the planes z = 0 and z = 4. Verify Stokes'theorem for a vector field F = xyi +x'j+ xzk.%3D%3D

given a vector field F=x2i+2zj-yk , curved surface area defined by x2+y2=25 bounded by z=0 , z=6 ,…

15 Evaluate F. dS, where F is the vector field x²i + 2zj – yk, over the curved urface S defined by x² + y² = 25 and bounded by z = 0, z = 6, y > 3. %3D 16. A region V is defined by the quartersnhon

15 Evaluate F. dS, where F is the vector field x²i + 2zj – yk, over the curved urface S defined by x² + y² = 25 and bounded by z = 0, z = 6, y > 3. %3D 16. A region V is defined by the quartersnhon

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

Solve this calclus

Question 15.

3, x = 0, y = 0.
Us över the stated curved surface.
15 Evaluate F. dS, where F is the vector field x²i +2zj - yk, over the curved
surface S defined by x² + y = 25 and bounded by z = 0, z = 6, y 2 3.
%3D
16. A region V is defined by the quartersphere x2 + y2 + z? = 16, z 2 0, y 2 0 and
the planes z = 0, y = 0. A vector field F = xyi +y²j+k exists throughout and
on the boundary of the region. Verify the Gauss divergence theorem for the
region stated.
17 A surface consists of parts of the planes x = 0, x = 1, y = 0, y = 2, z = 1 in the
first octant. If F = yi + x²zj + xyk, verify Stokes' theorem.
18 Sis the surface z = x² + y² bounded by the planes z = 0 and z = 4. Verify Stokes'
theorem for a vector field F = xyi +x'j+ xzk.
%3D
%3D

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