Use Green's Theorem to evaluate the line integral of F = (x6,3x) around the boundary of the parallelogram in the following figure (note the orientation). (X,Y) (x0, 0) Scx6 dx + 3x dy = (2xY) ·x With xo = 7 and yo || = 7.

Q: Evaluate ʃC F dr where C is the parabola y = x2 from (0, 0) to (2, 4) and F (x, y) =< −ysinx,…

A: Given a curve C is a parabola from (0, 0) to (2, 4)

Q: Let  f(x, y) = sin(15x2 + 3y2) Calculate the quadratic approximation of f at the point (0,0)

A: Given that,  fx, y=sin15x2+3y2 The quadratic approximation of the function fx, y at the point x0, y0…

Q: Find the point (x,y) at which the graph of y=4x2 +4x-8 has a horizontal tangent line

A:

Q: On the curve y = x², find a point at which the tangent is parallel to the chord joining (0, 0) and…

A: To find the point

Q: Find all value of x for the given function defined by y=2x³ – 6x where the tangent line is…

A:

Q: c) Use Part 2 of the Fundamental Theorem of Calculus to find the derivatives. d i) EevEdt dx dx J…

A:

Q: Write the function f(z) = z + 1/z in the form f(z) = u(r, theta) + iv(r, theta) (Answer is f(z) = (r…

A: f(z)=(r+r1​)cosθ+i(r−r1​)sinθ   Explanation:

Q: 3.1 (x+1) (x'+5x+2) ふeren ta ee

A: Topic = Derivative As per guidelines , At a time only one question can be answered.

Q: Let f (x, y) = e(2x-3y). Find the equation for the tangent plane to the graph of f at the point…

A:

Q: Find an equation of the tangent plane to the graph of F(r, s) at t F(r. s). - (3r4 1 + 1), (-1, 1.…

A: Introduction: Let z=f(x,y) denote the equation of a surface S in R3, and P=(a,b,c) denotes a point…

Q: Let f(x) = x² + 2x+1 a) Find the equation of the secant line between the points P and Q on the graph…

A: Let (a) To find the equation of the secant line between the points P and Q on the graph of , where P…

Q: Let f(x, y) = 5ex - Y. Find the equation for the tangent plane to the graph of f at the point (5,…

A: Given: fx, y=5ex-y. To Find: Equation of tangent plane to the graph of f at the point 5, 5.

Q: Find extrema of f (x, y) = 2x² + 4y² on the unit-circle x + y² = 1.

A: To find the extrema of the function ƒ(x, y) = 2x² + 4y² on the unit-circle x² + y² = 1, we need to…

Q: d dx y' z' y" z"

A:

Q: Show that the function f(x, y) = x² + 2xy is differentiable at any point (zo, yo).

A: Given function fx,y=x2+2xy The sufficient condition for differentiability If a,b be a point of the…

Q: (z)dz

A:

Q: 2(x + y)i + sin(y) 3. Find the line integral of Faround the perimeter of the rectangle with corners…

A: