The gradient of f(x, y) = x sin (y²) is the vector field F (x, y) = at (2,√π/6) and ending at (5,√/2). What is Sc F.dr? Sc F.dr = sin (9 2xy cos (y²) Let C be the straight line path starting

Q: For the vector field G = (yey + 3 cos (3x + y))i + (xeªy + cos(3x + y)), find the line integral of G…

A: We find the required integrtion using fundamental theorem of line Integral.

Q: Match the D.E. with a direction field: y' = t+y – 1, , y' = sin(t)sin(y), , y' = 2 – y, , y' = t(2 –…

A: NOTE: Horizontal axis is t-axis  .

Q: Suppose f(x, y) = sin( (a) Vf(x, y) = = (b) Vƒ(3, π) = 2y x T 2y 2y 2y cos cos 2) Con (2) 200m (20 -…

A: Given that , fx,y=sin2yx and u is the unit vector in the direction of 1,1.

Q: Find the direction field for the equation: y' = x + sin(y) + cos (x) at the point A = (0, pi3)

A: The direction field also known as slope field is used to graphically represent the solutions of…

Q: 3. Find the line integral fF.dr where C' is the circle of radius 5 in the xz-plane oriented…

A: The given vector field is .Find the value of line integral  as follows.The parametric surface can be…

Q: Let r (t) = The dot product r (1) · r ' (1) =

A: First differentiate at given value then take dot product

Q: Find the gradient vector field of f(x, y, z) = √√√4x² + 5y² + 2z²

A: