Find a function f: (-л, π) → R differentiable such that if p(0,0) = R(cos cos , sin cos , sin ) parameterizes the sphere S3 of radius R and cylinder C, then the function (0, z) = (cos, sin 0,z) parameterizes the F: S \ {0,0, +1} → C determined by -¹ ° F (0,0) = (0,f(p)) is a conformal diffeomorphism O O

Q: Let h be a differentiable function of z obtained from the parametric equations z = f(t), y = 9(t).…

A: Option  1  is true .

Q: a2f дхду' a2f 2. (a) If f (x, y) = x tany + ye-2*, find and What do you notice? дхду (b) If f(x, y)…

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Q: The tangent plane to the graph of the function f(x, y) = ey at the point with x = 1, y = -1, a) has…

A: Equation of the tangent plane to the surface

Q: Evaluate | f(x,y) ds where Cis the portion of the curve y = In x from the point (1,0) to the point…

A:

Q: Suppose f(x, y) = sin( (a) Vf(x, y) = = (b) Vƒ(3, π) = 2y x T 2y 2y 2y cos cos 2) Con (2) 200m (20 -…

A: Given that , fx,y=sin2yx and u is the unit vector in the direction of 1,1.

Q: 4. Compute the first fundamental form.

A: Given xu,v=u2-cosv,u+sint, cosv

Q: [15] (2) Consider the function ƒ: R² → R, ƒ(x, y) = x² − 2xy + 2y² Determine Vf. a) b) c) GIVEN: The…

A: Sine you have posted a question with multiple subparts we will solve first three subparts for you.…

Q: If Φ = xy^2 + 6 z^3 x^2, find  ∇Φ and |∇Φ| at the point (6,2,2)​ ​

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Q: Find the directional derivative of Du" f (2,1) in the direction of: a = 3i + 4j To f(x, y) = InGes…

A: Gradient of a function :  Let f be a differentiable function at  x , y  and let f x , y  have…

Q: For the function f(x,y) = 100 - x^2 - y^2 a) Draw the cross-section of f(x,y) with x fixed at x =…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

Q: Let h be a differentiable function of x obtained from the parametric equations a = f(t), y= g(t) .…

A: if x=f(t) and y=g(t) thendydx=dydtdxdt

Q: (b) In(2x2 + у — 23) %3D х

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Q: How did he get the value inside the circle f(x, y)=x² + sin(xy) Vf=x*+sin(xy)) i+ d(x²+sin(xy)), dx…

A: given ∇f(1,0)=2i+j we have to find the direction in which the directional derivative has some value.

Q: 1 : Evaluate f (x + 3y)dx + ydy where C is the Jordan curve given by the graphs of y = e, y = e- and…

A: ∫CMdx+Ndy=∫∫D(Nx-My)dA , where C is a closed contour enclosing the region D

Q: The equation of the tangent to the curve y=4+ sin' x at X=0 is O y = 4 O y = 2 O y = 6 O y = 3

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 2. Solve V'u = 0 for r<1, 0<z< T, u(r, 0, 0) = 0, a7(r, 0, 7) = 0, - u(1, 0, z) = z cos³ 0.

A: It is given that

Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: 2) Find the work of F = (x² - y² -4,2xy) on the semi-circle of radius 2 centered at the origin…

A: ∮F·dr=∮x2-y2-4dx+2xydy             =∬S∂∂x2xy-∂∂yx2-y2-4 dxdy               By applying Greens…

Q: The differentiable function f(*, y, z)= 1x² +7y +3z +4xyz tangent vector v, with i = (1,2,3) e R',P…

A: We have to calculate the derivative of f

Q: Find the directional derivative of f(x, y, z) = ((x+y+z)e², (x² + y²)e-²) at c = (1, 0, 1) in the…

A: The given problem is to find the directional derivative of the given vector function at point…

Q: 6. Given f(x, y) = 2x³y=x²y³, a) find the directional derivative of f(x, y) at (1, 1) in the…

A:

Q: determine wave direction in the function f(x,y) x^y — x²y³ decreases faster at the point (2,-3)

A: Wave direction in the function f(x,y)= x4y-x2y3 that decreases faster at the point (2,-3) is…

Q: Calculate Vf, V•f, V×f f (x,y. =)= xi+ y'j-* by the function

A: Introduction: The curl of the vector f(x,y,z)=fxi+fyj+fzk is given by ∇×f=∂∂xi+∂∂yj+∂∂zk×fxi+fyj+fzk…

Q: What are the coordinates of V'

A: For Triangle ∆TUV, the coordinates at point T is (-7,-6) at point U is (-8,3)  and at point V is…

Q: The directional derivative of f(x, y) = cos(x²y³ ) in the direction of the vecto v = 3i + 4j is Du…

A: The given function is: f(x,y)=cos(x2y3) So, ∇f(x,y)=∂f∂x,∂f∂y…

Q: 5. Compute the lenght of the curve u = t, v=0 from t = 0 to t = 1 using the first fundamental form.

A: Suppose, a continuous function is provided over a certain interval. The arc length is the length…

Q: = (u² - cos v, u + sint, cos v) x(u, v):

A:

Q: Given Yy - y = – ỹ Yy - y + y. - ỹ and (y — У )? [(Yj – J,) + ỹ, – ỹ )]² 2. %3D

A: Given that

Q: 5. Find all analytic functions f such that Ref + Im f = ry.

A: We need to find the analytic functions f such that Re f+Im f=xy. Consider the function of the form…