8. Evaluate •S.F.d F-dr where F(x, y, z) = (-7 sin(7x)-yz, π cos(ny)-xz, -xy) and C is any path that starts at (1,1/2,2) and ends at (2,1,-1). (a) 4 (b) 5 (c) 6 (d) 7 (e) 8

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: (1) (II) 10 F. 10 +t 10 10 -10 -10 (II) (IV) 10 10 斗t 10 t 10 -10 -10 a) y = 10e-t/2 cos 2nt b) y =…

A:

Q: (b) (2, -5π/6) (r, 0) = (r, 8) = y -1 -2 -3 -5 -1.5 (r> 0) ] ) (r< 0) 1 -1.0 2 3 -0.5 4 y -0.2 -0.4…

A:

Q: b) Find all the analytic functions for which Rez = Im f(z)

A: b) A function f(z) is said to be an analytic function at any point z=a if f(z) is differentiable not…

Q: "; Find y as a function of x if x?y" + 5æy' – 21y = x°, y(1) = 7, y(1) = -5. y =

A:

Q: Let g(8) = (2s – 1)°. Then g'(8) is 9'(1) is 9'"(8) is and g''(1) is

A:

Q: as a function of x when y =

A:

Q: What is the auxiliary equation for y"+by'+c=0, b & c is constant. What are the condition for this DE…

A:

Q: 7. Find the rectangular equation if r = 4 cos 0 + 4 sin 0 (a) (c) x² + y² = 4 x² + y² = 4(x + y) (b)…

A:

Q: (c) y/" + 4y = 3r cos(2r)

A:

Q: Find y as a function of t if 4y" +12y +9y = 0, y(0) = 6, y(0) = 6. 42 y(t) = 6 cos(-¹)+sin(-)

A:

Q: 72 3.(2.4) (1) Let c(t) = (sect, tant), — — < t < be a path. Find an xy-equation of this path. (2)…

A: Given that (1) Let  be a path. (2) Let  be a path.

Q: Find the line integrals of F = 2yi + 4xj + zk from (0,0,0) to (1,1,1) over each of the following…

A:

Q: Determine r (x) if r(x) = (arccot(x))".

A:

Q: 1. ('88 BC) The length of the curve y = x³ from x = 0 to x=2 is given by 2 2 A) [√₁ + x ²dx (B) √ √…

A: Given,.Formula for length of the curve is,