QUESTION 17 Find (1) (ii) F(x,y) dy F(x,y) ds where F(x, y) = 1 and C is the curve y=x²-Inx from (1,2) to (2,2 – In 2).

Q: Evaluate Se (5xy + x² + y²) dx + (x² - y)dy by using Green's theorem, where C is a closed curve that…

A:

Q: etermine Z J f(x,y) ds with curve C is the curve of the circle x+y² =4 from (0, 0) to (- nd fly d

A: ∫c f(x,y) dsC ;  x2+y2=4   from   (0,0) to  (-3   , 1)and  f(x,y) =x(y+1)+y

Q: Evaluate [F·dr if F(x, y)=(4e³)ī +(4xe³)j and the curve C' is line segments going from (0,0) to…

A: To evaluate ∫C F⇀·dr⇀ if F⇀x, y=4eyi⇀+4xeyj⇀ and the curve C is line segments from 0, 0 to 5, 4 to…

Q: Consider the following. r,(t) = (2t, t2, t³), r;(t) = (sin(t), sin(3t), 5t) Find r',(t) andr'2(t).…

A:

Q: Question 9 Find the equation of the tangent plane to the function z=2x-3y + 4(x - 1)² + 5(y- 1)³ at…

A:

Q: Find the length of the curve described by y = V sec* t – 1 dt, - sI 4 4 (a) 4 (b) (c) (d) 2/2 (e) 1

A:

Q: Evaluate F dr where F(x, y, z)=(x, xy, yz) and C is the curve r (t) = (t, t

A:

Q: The cartesian equation of the curve x = 1-t,y= t is : (a)y = 1– x², x20 (b)y =1-x ,x 2 0 (c) x = 1 –…

A:

Q: The cartesian equation of the curve x = vt ,y= 1-t is: (a)y = 1 – x2, x 2 0 (b)y = 1 – x ,x > 0 (c)…

A: Given:-paametric equation:x=t y=1-tsince we have to find the cartesion equation

Q: 2. Find parametric equations for the line that is tangent to the curve 7(t) = (cos(t), et,4 – 3t) at…

A: Solution:-

Q: (6) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

A: Orthogonal trajectory curve of a family of curve is defined as a curve which intersects every member…

Q: Determine the derivatives, dy da dy da (1) y=e¹ ⇒ (2) y=x4 ⇒ dy da Y of the four given curves.

A: The functions are (1) y = ex(2) y = x4 To determine: The expression of the first derivative dydx.…

Q: Suppose the two curves r(t) = (t,0, 1 + e' sin(t)) and q(s) = (0, s, vs² + 1) lie entirely on the…

A: According to the given information, consider the given two curves:

Q: 2) (i) Find the equation for the tangent plane to 2 2 z=f(x, y) = 2 x + 3y at the point (2, 2, 20).…

A: The equation of the plane is z=fx,y=2x2+3y2

Q: Problem X: Evaluate [ (x In y + y)dx +(x +1+)dy where C is the portion of the curve 2y y =x' - x' +4…

A: Given ∫Cxlny+ydx+x+1+x22ydyWhere C is the portion of the curve y=x3-x2+4 from 0,4 to 2,8.

Q: Evaluate |-y dx+x dy , where C consist of the curves along the horizontal line from (-4,4) to (-2,4)…

A: The given integral is: ∫C -ydx+xdy Where C consists the curve along the horizontal line from -4,4 to…

Q: • Let S be the graph of f(r, y) = r² + y² – 2r + y for (r, y) E D = {(r, y) :2² + y² < 4 and z + y 2…

A: The function is fx, y=x2+y2-2x+y The region D is x, y: x2+y2≤4 and x+y≥0 The edges are x2+y2=4 and…

Q: 5. Verify Green's Theorem in the plane for F = (xy + y²)î + (x – y)f and the curve C is as shown in…

A:

Q: find and sketch the point of shortest (or longest) distance from the origin of curve…

A: We need to find and sketch the point of the shortest (or longest) distance from the origin of curve…

Q: Scetch the curve y and calculate , f(2) dz: a) 7(t) := t+i cos(t), te [0, 27], f(z) = R(2); b) y(t)…

A:

Q: x(t) = t°; y(t) = t® is not a parameterization of the ,3. curve y = x Select one: True False

A: By definition, a function is a special case of a relation between the members of two sets. It is a…