Let F(x, y, z) = . Let C be the curve in R^3 given by r(t) = , for 0 ≤ t ≤ 1. Evaluate The integral C F · dr.

Q: If g(s,t) = f(s^2 - t^2, t^2 - s^2) and f is differentiable, show that t(∂g/∂s) + s(∂g/∂t) = 0

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Q: G(x,y)= (x+3y) / (x^2 - y^2 ) Sketch the domain

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Q: What is the largest value of the function f (x,y) = x³y³ on the curve x4+ y^= 1? O 2-1/2 0 3√4 01…

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Q: Let be a curve in the xy-plane. Find d'y dx² -|(x, y)=(1, 1) = _ 6x³3 + 19y³ = 25 તે પુ da²(x,…

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Q: Find f. f'(t) = 8 cos t + sec²t, -π/2 < t < π/2, f(π/3) = 2

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Q: Evaluate d:/dx on the surface x: + + x²y®=² = 3 at the point (1, 1, 1).

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Q: integral f t^3 In t dt

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Q: SOLVE BY LINEAR METHOD - y'- 3 X Y = x 3 cos (x)

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Q: Find the Felative Maximum vasve of Fx,x) = x*- y, Subuicct to the Construint X-Y=24.

A: The given function is as follows. fx,y=x2-7y2 the given constraint is as follows. x-y=24y=x-24 The…

Q: Evaluate ∮C (x + 3y)dx + ydy where C is the Jordan curve given by the graphs of y = e^x, y = e^−x…

A: ∮Cx+3ydx+ydy Where C:y=ex, y=e-x, y=e-1

Q: Let f(x, y, z) = x^2 + y^3 + z^5 and let u =. Find the directional derivative Du f(x, y, z).

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Q: what local linearizatoin of the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1)  (show all steps…

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Q: DIfferentiate the functon. +22) #26) ge) =/1+ Int %3D Inx #H) y= In tart x In tanx

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Q: 2x'y+x?y? + 3xy³ 16x4 – y4 if (x, y) # (0,0) Let f(x, y) = if (x, y) = (0,0) Determine the set of…

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Q: Let f(x,y)=(x^2+y^2 +1)^1/2. Find fx(0,0) and fy(0,0)(if they exist),and decide if f(x,y) is…

A: The given function f(x,y)=x2+y2+1