comment it ASAp please
Calculate • (-3x, 2y). Nds where C is circle of radius 5 centered at the origin...
44. The vector field F has F 7 everywhere and C is the circle of radius 1 centered at the origin. What is the largest possible value of F dr? The smallest possible value? What conditions lead to these values? 44. The vector field F has F 7 everywhere and C is the circle of radius 1 centered at the origin. What is the largest possible value of F dr? The smallest possible value? What conditions lead to these values?
(b) Evaluatex + 2y ds where C is the portion of quarter-circle centered at the origin with the clockwise rotation from (-3,0) to (0,3) which in turn is followed by the line segment from 0,3) to (6,2). (10 marks) (c) Let F = (2x2y, ya), a closed curve C and let D be the region enclosed by the curve. The region R is in the first quadrant bounded by the r-axis, the line x = 1 and the curve y...
2. Consider the circle of radius 9 centered at the origin in the ry-plane. It can be described by the equation 2 +y2 81. The sphere of radius 9 centered at the origin can be created by rotating the curve y v81- about the a-axis. (a) The volume of the sphere can be calulated using a definite integral. Set up that definite integral, but do not solve it. (b) Complete the calculation of the integral. 2. Consider the circle of...
Given a positive integer n and a real number θ E (0,7), prove that sin n θ 2 sin θ where γ is the circle of radius 2 centered at the origin, oriented counterclockwise. Given a positive integer n and a real number θ E (0,7), prove that sin n θ 2 sin θ where γ is the circle of radius 2 centered at the origin, oriented counterclockwise.
3. Consider the vector field F(x, y) + 2y F dr, where C is the circle (r-2)2 +y2 = 1, oriented counterclock (a) Compute wise (Hint: use the FT of line integrals. We could not use it for the circle centered at the origin, but we can use the theorem for this circle. Why?) (b) Let 0 be the angle in polar coordinates for a point (x, y). Check that 0 is a potential function for F 3. Consider the...
c. Evaluate ,f(z) dz with า the circle of radius 1 centered at the origin and traveled once counterclockwise ˊ们: (1-2 For real twith-1 < t < 1 and +12)-1 Explain why f(:)) has an expansion of the form in C , let f(z) be defined by fG)- a. b. Compute Uo(t), Ui(t), and Uz(t) in terms of t. c. Recalling that t is a real number smaller than 1 in absolute value, find the radius of convergence of this...
Trying to rewrite integrals using Green, Stokes or Divergence theorems. Don't have to evaluate. (b) fe (zz,-yz, ez? – y2). dr where C is the curve on the unit sphere satisfying the equation ø= 3 (1 + £cos(20)), oriented in the direction of increasing e. r .nds where S is the surface composed of spheres of radius 1 and 2 centered at the origin, with n on the radius 1 sphere directed toward the origin, and n on the radius...
Evaluate: UnitCircle where the contour is the unit circle centered about the origin.
1) Suppose a dart board is a circle of radius one centered at the origin. A player throws darts many times and hits the board every time, recording where the dart hits. The player then finds the probability density function of where they hit on the dartboard is given by f(r,y) r2 +y -(r2 y)) a) Based on your knowledge of probabilities determine the value of C given that the player never misses the dart board. 1) Suppose a dart...
Help me please ax ay a) Calculate le centered at the origin, oriented counter clock wise ) caleulate Fdhere Ca i the boundary of he rectanale ot 44oented counterclocknise c) Let C, be the circle of radius 크 centered at the point a0.2); let Ca he the cirele of radivs & centered at the axigin let s be the square of side 14 centered at c ith side di where Ca is the unit cinele in thexy-plane paralel to the...