1. (10 points) Evaluate j F dl for the vector function F(3x y2)a, from P1 (5,6)...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
For the form a 2ryda (2 -y2) dy, define the function f(x,y) = 10 where c is the straight line path from (0,0) to (x, (a) Compute f and then df (b) Is df = a? Why or why not? (c) Evaluate J df. Is this the function f? Why or why not?
For the form a 2ryda (2 -y2) dy, define the function f(x,y) = 10 where c is the straight line path from (0,0) to (x, (a) Compute...
2. (8 points) Let F- try - vy2. Evaluate the line integralF dl using the f ollowing paths: a) (2 points) Going from 0, 0 to r 2,y 1 along the straight line y b) (2 points) Going from 0, 0 to r 2,y-1 along the parabola y c) (2 points) Going from 0,y 0 to 2,y 1 by going first along a vertical line from0,y0 to x-0, y-l then along the horizontal line x , y-i to x-2, y-1,...
1. The position vector r acting from point A(-2,-5,6) to B(4,3,-1) in Cartesian vector form are shown below. Determine the distance between points A and B and t angles A(-2,-5,6) y X B(4,3-1) 2. The diagram below shows a force F= 250N is applied to the chord which is attached to the top of a 6m pole. Express force F as a Cartesian vector; and determine its coordinate direction angles. z A(-2,-5,6) F=250N y *B(4,3,-1)
let F(x,y) = 3x^2y^2i+2x^3yj and c be the path consisting of
line segments from(1,2) to (-1,3), from (-1,3) to (-1,1), and from
(-1,1) to (2,1). evaluate the line integral of F along c.
Let F(x, y) = 3x²y2 i + 2x’yj and C be the path consisting of line segments from (1, 2) to (-1,3), from (-1, 3) to (-1, 1), and from (-1, 1) to (2, 1). Evaluate the line integral of F along C.
(a) Find the flux of the vector field F=yi-xjtk across the surface σ which is 4. x2 +y2 and below z the portion of z 4 and is oriented by the outward normal. _t7г (b) Use Stokes' Theorem to evaluate the line integral of J F.dr of F--уз ì_x3 j+(x+z)k where C is the clockwise path along the triangle with vertices (0,0,0). (1.0,0)and (1.i.o) aong the thiangle with(i) t)
(a) Find the flux of the vector field F=yi-xjtk across the...
b- Consider the vector field F(x,y,z)= (3x²y2-3ze, 2xy +2sin z, - 3x02 + 2ycos z). (a) if f(x,y,z) = axºy2+be*2 + cysin z then a =......, (b) Use the fundamental theorem of LINE INTEGRAL to evaluate Y = SF-di along the curve defined by the parametrization F(t)= (1, sint, t-T) for Osts. Y = ...... b Choose... Y = Choose.... Choose... Choose...
Please help me how to solve this problem
Find the circulation of the vector field F(x, y) = P(x, y)i +
Q(x, y)j where P(x, y) = [2 − y] / [9x^2 + (y − 2)^2] + [−2 − y /
[9x^2 + (y + 2)^2] , Q(x, y) = x / [9x^2 + (y − 2)^2] + x / [9x ^2
+ (y + 2)^2] , around the simple closed curve C = C1 ∪ C2, where C1
is...
For a vector field F(x)(2yarctanx)j find a function f such that F,y)-V/ h(2yarctanx)j find a function f such that F(x,y)-U For a vector field F(x,y)- 1+x2 and use this result to evaluate dr, where C: rit2, osis1
For a vector field F(x)(2yarctanx)j find a function f such that F,y)-V/ h(2yarctanx)j find a function f such that F(x,y)-U For a vector field F(x,y)- 1+x2 and use this result to evaluate dr, where C: rit2, osis1