Use Gauss' Divergent Theorem to calculate F. dS where F = (2x + sen (et1)) i+3y²j+ cos(z²)k and S is the boundary of the solid E = {(x, y, z) E R³ | x² + y? < 2 e -1
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- Which of the following is a linear DE of order one in x? A. (sec² x - y)dx + (x−y)dy = 0 c. (x-y²dx+cos3x³dy=0 dy_y+2y² D. (x-y)dx +(y-x² dy=0 x-3y B. inx + 6x² D. y = C1 + C₂x² + C3COSX + C4Sinx + 6x² dx What is the orthogonal trajectory of the family of parabolas having their vertices at the origin and their foci on the y-axis? A. 2x² + y² = k² B. x²-2y² = k² C. x² + 2y² = k² D. 2x² - y² = k² Which of the following CANNOT be solved by method of unUse the Green's Theorem to evaluate the line integral f, FdT where F = (sin(x²)–2x²y) i´+ (cos(y²) + x³) i and L is a closed curve that consists of a part of the parabola y = x² and the line y = 1, with –1 < x <1 oriented counterclockwise. 6.This is a surveying course
- F(x, y) = (2xy³ + 3)i + (3æ²y? + 2e²)j is conservative by finding a potential function f for F, and use f to compute F. dr, where C is the curve given by r(t) = 2 sin" ti+ 2t sin10 5tj for 0Use the map G(u, v) = (1, 1) to compute f (x + y) dx dy, where D is the shaded region in the figure. Assume a = 8, b=16, c = 6. b 1 x a y y=cx D y=x (Use decimal notation. Give your answer to three decimal places.) (x + y) dx dy = XUse a parameterization to find the flux(a) Calculate the line integral of F ==°yi + y°j+ z*k along the straight line path from (1, 1,0) to (4, –2,0). (b) Calculate the line integral of F from (1, 1, 0) to (4, –2, 0) but along the path y = (-1²+6)/5, z = 0= (-2y)i + (x)j – (3)k and S is the Vx2 + y2 , 0compute the line integral . parametrizations.Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,