6) Let F(x, y) = [sin(y)- y² + 1] lx cos(y) - 2xyl Is F conservative? If so, give a potential function for F.

Q: (2) Let F(x, y) = (cos(y)+2x, -x sin y+1). Show that F is path independent by finding %3D a…

A: For the given vector function to be independent, it must be derived from a potential scalar function…

Q: Find f if ƒ"(t) = 2et + 3 sin(t), ƒ(0) = 2, ƒ(π) = 5. f(t) =

A: f''( t ) = 2et + 3sint f( 0 ) = 2 f( π ) = 5

Q: Let f"(t) = /t – 2 cos t. Determine a general f(t). -

A: Given : f'''t = t - 2cost

Q: Find f. f(t) = f"(t) = 7et + 3 sin t, Need Help? Read It f(0) = 0, f(π) = 0

A:

Q: Let u(æ) = sin(x) and v() = a = 18 and f(x) (*)a u (2) -| v (2) = u'v – uv f'

A:

Q: Find a potential function for F or determine that F is not conservative. F = (cos(z), 16y, -x…

A: The vector field given in the question is: F = <cos(z), 16y, -xsin(z)> Hence, F1 = cos(z), F2…

Q: Find f. f "(t) = 2et + 5 sin t, f(0) = 0, f(x) = 0 f(t) =

A: We can solve the given problem using the concept of application of integral.

Q: Find f. f(t) =|| f"(t) - 3et+ 5 sin t, f(0) = 0, f(T) = 0

A: To find f.f''t=3et+5 sin t, f0=0, fπ=0

Q: Use the gradient to find the directional derivative of the function at P in the direction of Q f(x,…

A:

Q: Find f. f"(t) = 5et + 4 sin t, f(0) = 0, f(1T) = 0 f(t)

A: topic- differential equation