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: given f(z)=u(x,y)+iv(x,y) is an analytic function where u(x,y)=x^3-3xy^2. find f(z)

A: We have to find .

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: Calculate the directed derivative of the function f (x, y) = (y^2)/x on the ellipse 2x^2 + y^2 = 1…

A: The given function is fx,y=y2x and the ellipse 2x2+y2=1 Directed derivative,…

Q: Exercise 8. let C be any closed simple curve and f(z)=lz+il. Then the integral of f(2) over C is 0.…

A: Given C, any closed curve.  And f(z)=|z+ i|

Q: Let f be analytic in a region G. If f(g) lies on the parabola u=v^2, prove that f is constant in G.

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Q: Let f(x, y) = x* /I Evaluate f(3, 0)

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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: Let f(x,y)=tan^-1(y,x). Find and simplify fx and fy. Then find and simplify fxx, fxy, and fyy.

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Q: Find the equation of the tangent plane to the surface z=e^x+y+y^3+9 at the point (0,1,12). z=

A: The equation of the surface is z=ex+y+y3+9. We have to find the equation of the tangent at a point…

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: 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: Let f : R2 → R with f(x,y) = px^2 + y^2. Sketch the graph of f. Prove that f is not differentiable at…

A: Given f(x,y)=px2+y2

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: Let F(x , y , z) = g(y) + h(z) + 5 In(x - 2) , where g(y) and h(z) are differentiable functions of…

A: If a function is a function of more than one independent variable then the derivative of this…

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: Let X ~ Uniform(-1,1) and Y = X² , find the CDF and PDF.

A: Use the following definitions, to obtain the solution. The cumulative distribution function of a…

Q: Find the absolute extrema of f (x, y) = x^2 + y^2 + xy on the disk x^2 + y^2 ≤ 1.

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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: Find the parametrization of the curve defined by the intersection of the two surfaces y = x^2 − 3z^2…

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Q: Which of these relations on the set of all people are equivalence relations? Determine the…

A: Note: We will only answer up to three sub-parts as the exact one is not specified. Please resubmit…

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: 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

Q: II. Let f(x, y, z) = z° sin a + Determine 2 dydzərəz'

A: We know, ∂2f∂y∂x=∂∂y∂f∂x