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: Let f(z) be an analytic function defined on the complex plane, where z=x+iy and ii is the imaginary…

A: The derivative of a function in complex analysis is defined similarly to that in real analysis.For a…

Q: Use the cauchy-riemann conditions to determine whether the function f (z) = ((x ^ 3) + x(y ^ 2)) + i…

A: Cauchy-Riemann  : Let f(z)=u(x, y)+iv(x, y) be a complex valued function. Then the Cauchy-Riemann…

Q: 4xy* :- find f,,f, at point (4,1) for f(x,y) = x’e**Y

A: I have used partial differentiation

Q: Find V· (V × F), if F(x, y, z) = 3e**i+3xe'j – 3e²k. - V·(V × F)

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Q: f(x,y) = arctan(2x-3y)+ Find the domain and sketch it. In(x^2 +2x+y^2).

A: To find the domain of the function f(x, y), we need to consider the values of x and y that make the…

Q: Write f(z) in the form f(z) = u(x, y) + iv(x, y). a) f (z) = z^3 b) f (z) = 1/z^2

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Q: Let g(u) be a differentiable function, and let f(x, y) = g(x^2,y^2)   Find the direction of…

A: Given that gu be the differential function and let fx,y=gx2,y2 We have to find the direction of…

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

A: G(x,y) = x + 3yx2 - y2 The denominator cannot be zero. Therefore, x2 - y2 ≠ 0(x+y)(x-y) ≠ 0x ≠ -yx ≠…

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: 11- Find the moment of inertia about x-axis bounded by the curve y = 6- x² and the line y = x + 1

A: The given information in the question is the curve y=6-x2 and the line y = x + 1. The objective is…

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 one normal vector of the tangent plane to f(x, y) = cos(x² +y²) at point P(1,1, cos 2).

A: As we know the expression of the normal vector to the tangent plane at a point on the curve can be…

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: Consider a differentiable function p(x,y) with the properties below. Use these properties to answer…

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Q: YDiscuss the integrabilty of the function f(x) = on [0,7).

A: We need to find the integrability of the function and find the integral of it.

Q: Q6: A: If f(x,y)=ycos⁡x+xe^y.find f_x,f_y,f_xx,f_yy,f_xy B: Find the derivative of…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

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).

A: The directional derivative Du​f(x,y,z) is 64/81​.Explanation:Step 1: To find the directional…

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: Let f(x, y) = 2x^3+5y. Find the linear approximation of f(x, y) near (1,5), and use it to estimate…

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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: et X=R^(2) and C={(x y)in R^(2):x>=0 y=0}. Show that C is not a generating cone.

A: Given: Let   and .  To show that C is not a generating cone.

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