Given that F = xz i − 2yz j + x2yz k. Find the followings at (1, 1, 3): (a) div F.  (b) curl F.  (c) r. (r× F).

Q: Consider the function w = √√x² +: dw b) Find əs 6z where x = sinp, y=p+3t-4s, z = and p = 1-2t.

A: I have explained everything with in the solution. Please go through that.

Q: vinarixinvaxana Pic г.) 4. Find Brune fronor. [

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Q: 35. f(x, y) = x² + 2y² – x; R is the disk x? + y? < 4.

A: fx,y=x2+2y2-x which is bounded by R, R:x2+y2≤4, where R is a disk Partially differentiating fx,y…

Q: I x In y dA, R = [0, 3] × [1, e] 43.

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Q: Find div F and curl F if F(x, y, z) = 16yªz³i – 17x7zºj − 3xy¹k. div F= curl F=

A: Given: F(x,y,z)=16y4z5i-17x7z6j-3xy7k. To be find: div F∇.F and curl F∇×F. Concept: for a vector…

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A: While finding partial derivative in multivariable function, if we have to find the partial…

Q: xy² dA, R = [0, 2] × [- 3, 3] Find x2 + 1 R

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Q: b) Evaluate the value of I = S(e³y – 3x)dx + (6xey + y)dy, where C' is the parabola - C (0, 0) to…

A: One has to solve it by Green's Theorem.

Q: Evaluate xy dx + (x+ y)dy along the.curve y = 4x from (- 3,36) to (- 2,16). C xy dx + (x + y)dy =] C…

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Q: alla Find xy² R2² -dA, R= [0, 4] × [ - 2,2] x² +1

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Q: (b). Use Green's Theorem to evaluate SF. dr. F(x, y) = (e³x², 2xy), where C is the triangle from…

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Q: Given that F = (2x + y2)i + (3y – 4x)j. Verify Green's theorem for F.dr around the triangle formed…

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Q: The curl of f(x,y,z)=xyzj is =.

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Q: √2-y² X √x² + y² dx dy

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Q: 4. Evaluate both sides of Green's theorem, for: F = (-x²y,xy²) where C is shown in the following…

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Q: c). Evaluate √√x² + y² ds along the curve r(t) = (4 cost)i + (4 sint)j +3tk, -2x≤t≤2π.

A: We solve the given line integral.

Q: dx dy, where D is the disk x2 + y² < 9. (x² + y?)3/2 Evaluate

A: The given integral is,

Q: Find V. (F × G), if F(x, y, z) = 5xi +j+ 7yk and G(x, y, z) = xi+yj – zk. - V. (F × G) =

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Q: Use the Midpoint Rule with m = n = 2 to estimate the value for R= [0, 4] × [0, 6]. √ √ ( 3x + 2y) dA…

A: Sol:- To use the midpoint rule with m=n=2, we need to divide the rectangle R into 4 smaller…

Q: Let x = (-2,7,-7) and y = (1,6, 6) be in R°. Compute the following: x + y = ( -5x x – y = ( -5 x +…

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Q: Find a. b. [ f(z)dz. if C 1 f(z) = z sin z f(z) = 2² - z+1 z²(z - 1) and C:|2|= 1 to positive…

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Q: Given z = f(x – y, 2x – 2y, 3x – 3y). Show that dz dz 0. dx fie +

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Q: + 4z 53. Use (7.8) to evaluate dz around the circle |z – 2i| = 2. - z4 + 8z2 + 16

A: Given,  ∮z3+4zz4+8z2+16 dz  around the circle z-2i=2

Q: Find the value of V. (V × A) where A = x²yî – 2xyz²j+ 2xy²zk.

A: The partial derivative of a multivariable function with respect to a variable is the derivative of a…

Q: 1. (1+ V)²dx 2 2. (교2-z) dr (r-1 +x)2 3. xp-

A: solve the following

Q: Consider the function r(t) = (2 cos t)i + (8 sin t)j. Find all the points on the function at which r…

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Q: da J 5—4г — 2:а? 5 – 4x 2.x 2

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Q: 6e? Evaluate dz by residue theorem, 9z4 + 45z3 where C'is the contour z = 2

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Q: ry? Find I.A. -dA, R= [0, 4] × [ – 1, 1] г? + 1

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