Show that Si2 f dæ + g dy + h dz = S - (4xy³z*dx + 6y?x?z4dy + 8z°y³x²dz) is independent of path: (-1,-5,-3) J(5,–1,2) c(-1,–5,-3) _ J(5,–1,2) ah -242,2,3 %3D ag az af %3D az –16xp3_3 ah |- 16xy3,3 -12y-4 ag Therefore curlF = C-1,-5,-3) Ss,-1,2)- (4xy*zªdx + 6y²x²z*dy+ 82°y%x*dz) = |

Q: Use the chain rule to find and, where First the pieces: əz dx 2x+y ?х მყ dy მა = дz Ət || 2 And…

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Q: Form 2 of the chain rule. Do the following problems: A. Let z = u² + v²; u = 2x + 7, v = 3x + y.…

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Q: (1,2) 6. Evaluate 0,1 (x²-y) dx + (y² +x) dy along a straight line from (0,1) to (1,1) and then from…

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Q: 12. Let F(x, y) = (sin(y)), and let P represent the path that goes in straight lines from (1, 0) to…

A: We see,        = (ysin(xy), xsin(xy))        = (dx, dy) Hence,     = (ysin(xy), xsin(xy)).(dx, dy)…

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Q: If f(r, v)= +y-2y, find fa (2, 1), f (2, 1), fay(2, 1) and fy(2, 1).

A: Given a function f(x,y)= x3+x2y3-2y2 Now, fxx= ∂2f∂x2=∂∂x∂f∂x fyy= ∂2f∂y2=∂∂y∂f∂y…

Q: 5. Find the linear appoximation for the funciton f(x, y) = (ro, Yo) = (3,0). x-y xy+1 at the point

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Q: 2. We showed in class that EL (: - T)(y: – 9) can be written as a linear combination of ys: B1 = Gi…

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Q: Let -2xy – 3yz – cz, x = st, y= e", z=t? Compute ди (4,-5) = ds dw (4,-5) =

A: The given function.

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Q: + x(x*+ zy² + ig) dy= luy) dy 2. 2. 2) 3(x y) dx -

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Q: (D7 + D° – 2D5 – 2D4 – 7D³ – 7D² – 4D – 4) y = 0 | (D4 – 3D3 + 4D)y = 6 + 80cos2x y" + 4y' + 3y =…

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Q: Let P denote the path that goes in straight lines from (0,0, 2) to (0,1, 2) to (1,1, 2) to (1,0, 2)…

A: Given: F→(x, y, z)=(1-z)5yxez-2z15+14

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) =i - 3tj + K 2 (a) r'(t) (b) r"(t) (c)…

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Q: se Green's Theorem to evaluate SC (5y-9x)dy-(yx-x³)dx where C is shown below

A: Follow the procedure given below.

Q: Let u = u(x, y, z.) be determined near (1, 1, 1) by x²y³z²u³ + 2xy²u³ - 3x³z²u=0, u(1,1,1) = 1. Find…

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Q: Solve for the higher order DE number 2

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Q: Evaluate (r(t) · r1 t))l-2 where r1(t) = (t³, t“, t³), r(2) = (0, 3, 1), and r' (2) = (2, 4, 5) 42 O…

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Q: Show that Sa fdx + gdy = Sa - (16x*y²dx + 8yxʻdy) is independent of path: (10,5) –2) (10,5) ,-2) 4…

A: We are given a line integral as follows : ∫1, -210, 5 fdx+gdy=∫1, -210, 5 -(16x3y2dx+8yx4dy)   First…

Q: (14,-9) (7,-10) (14,-9) Show that f(fdx+ gdy = f(10) 12x²y dx + 16y3x³dy is independent of path:…

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

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Q: Q.3 a) If acceleration components of an electron are given by d²x - b d²y 0, dt dy dx b- = a dt dt?…

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Q: 2. Show that the equations f(r, y,P. q) = 0 and g(r, Y.P. q) = 0 are compatible if %3D %3D a(f,g)…

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Q: Let f(u, v) = (tan(u - 1) - ev, u²-v²) and g(x, y) = (ex-y,x-y). Use the Chain Rule to find…

A: Given functions: fu,v=tanu-1-ev,u2-v2gx,y=ex-y,x-y To find: Df∘g1,1 Concept used: If the functional…

Q: -20x-2) SS f(x.y) dy dx + f(x.y) dy dx= f(x.y) dx dy, then g(6a)+h(a)= if (4)6 0

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Q: Use Yule-Walker equations to determine the autocovariance function of a stationary ARMA(2,1)…

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Q: Show that f10 fdx + gdy = S6 10 5a*y²dx + 2yx³dy is independent of path •(11,–7) ,-10) • (11,–7)…

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Q: (ii) Suppose z = f(x, y), where x = g(s, t), y = h(s, t), g(1,2) = 3, gs (1, 2) = −1, gt(1, 2) = 4,…

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