Let F =< xy,5%, 4y >. Use Stokes' Theorem to evaluate So Ẻ · dř, dr, where C C is the curve of intersection of the parabolic cyliner 2 z = oriented counterclockwise as viewed from above. y² -x and the circular cylinder x² + y² = 1,

Q: 4. F(1) + Fib(2) = %3D 5. F(2) + Fib(3) = %3D 6. F(1) + F(2) + F(3) + F(4) =

A: We will answer the first three questions as per our guideline. Please resubmit the other questions…

Q: 4. First, sketch a picture of the line which passes through P = (1, 1, 2) that is perpendicular to…

A:

Q: Use Stokes' theorem to evaluate Ĝ - dĩ, vhere Ĝ(1, Y, 2) = (2r, y,0) and D is any closed curve.

A:

Q: Find the tangent plane to the equation z = 7e²²-2y at the point (4, 8, 7) 2 II

A: Given:The equation is  and the points are .To Find:The equation of the tangent plane through  is…

Q: a) Find the equation of tangent line of curve that is given by parametric equations X = 3cost + sint…

A: (a) Given  parametric form of curve is…

Q: Find the equation of the plane tangent to the surface z = 3x² + y² at (1, 1, 4).

A:

Q: The equation z = f(x,y) = y +x -3y defines a surface. What is t- equation of the tangent plane at…

A:

Q: Find the equation for the tangent plane to the surface z= 7x2. 10y² at the point (2, 1, 18). O 2x +…

A: Equation for the tangent plane to the surface z=f(x, y) at the point (a, b, f(a, b)) is given by

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. x = u…

A:

Q: Let r(t) = (et, et sin t, et cos t).  Find the equation of the plane that is normal to the curve at…

A:

Q: 8) Given z =f (x.y) =1- (x² +4y2) ,Find : a)The vector function, 10 normal to the surface of f at…

A: This is problem of vector calculus.

Q: Using the formula, Area = " y(t)x'(t)dt, find the area under the following parametric curve. x = 2…

A:

Q: the appropriate that should be applied the differential equation 4 - 54 - 5 xyở ³ 2 K

A:

Q: What is the radius of a hemisphere with a volume of 144,000m cubic centimeters? radius = cm

A:

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. x = u…

A:

Q: The slope of the surface z = xy² in the x- direction at the point (2, 3) is O 12 O 8 O 1 O 9 O 10

A: The slope of the surface z = f(x,y) in the x-direction at (x0,y0) is given by [∂z/∂x](x0,y0) =…

Q: Determine the centroid of the following Fig from X and Y axes. Y, 30 centT1 2 CentQ1 -4 -3 -2 -1 1 2…

A:

Q: Consider the curve F(t) that represents the intersection of the surfaces x + y? -1=0 and y= 2x a.…

A: Given: The curve r(t) represents the intersection of the surfaces x2+y2-1=0 and y=z/2x.