Q1- The divergence of the function f-(rs cos 0)e, in spherical coordinates is......

Q: ? Find the divergence of the function in spherical coordinates f = (r*sin 0)e,

A: First we will look at divergence of a function in spherical co-ordinates. Let F=Fr er+Fθ eθ+Fφ eφ…

Q: Prove that fe, r*dx + rydy = 0 where Co is the line segments from (0, 1) to (0,0) by using…

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Q: 7. Find the length along the parametric curve defined by v(t) = (t, In(cos(t))) from t = 0 andt=.…

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Q: 1. If the parametric curve $x=f(t), y=g(t)$ satisfies $g^{\prime}(1)=0,$ then it has a horizontal…

A: TRUE Slope of the curve, when in parametric form = dy/dx = g'(t) / f'(t)

Q: ди ди ду ду Find the cauchy-riemann equations of, f (z) = | z | sin z. əx' dy'dx' ðy,

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1. In…

Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (c) Determine the…

A: Here is the solution of the given problem.  To solve this problem we use simple concept of…

Q: Find the area of the part of the eircle r-4 sin that lies within the sector 0 50s 87 -2/3 3 + V3 3.…

A: It is given that,r=4sinθ, that lies within the sector 0≤θ≤π3we have to find the area of the part of…

Q: 1 Evaluate f - dz over the unit circle in counter-clockwise direction using the parametriza- tions

A: To evaluate, ∮1zdz over the unit circle counter-clockwise

Q: Find the arc length traced out by the endpoint of the vector-valued function 7(t) = t cos t î + t…

A: Solved below.

Q: 7. Given the space curve er(t) = (4 sin t ,4 cos t , 10t), Find T, N, B, and t (torsion)

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Q: Find the parametrization of the tangent line to the space curve r(t) = (e" , sin(t), (t + 1)-³) at t…

A: Given that  r(t)=(e^(4t),sin(t),(t+1)^(-3)) at t=0 We have to find out the parameterization of the…

Q: Is the differential 2re sin ydr+e cos ydy exact? If yes, then the funetion f from which it is exact…

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (b) Reparametrize R using…

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Q: The function f (2) e? at z=0 %3D has pole removable singular point None essential singular point

A: The given function is  f(z) = ezz4

Q: 2. Consider the following vector-valued function 7 (t) = (t sint + cos t, sin t – t cos t, v6t?)…

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Q: Q1- The divergence of the function f= (r cos 0)e, in spherical coordinates is..........

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Q: . If f = In(x² + y² + y³ ) then find the divergence of falso find its magnitude at 2 3)

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Q: Find the tangent plane to the equation 5y cos(2x – 4y) at the point (4, 2, 10). - = Z z =

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Q: Q1- The divergence of the function f = (r5 cos 0)e, in spherical coordinates is...

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Q: Use Green's theorem to evaluate (2y dx-x dy) around the closed curve C. 27 (2,8) 8. 4. C. -2 (1,-1)

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Q: Consider a new curve Č parametrized by r(t) = (cos t esint, sin t- cos t), 0 <t <I but with F still…

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Q: (10) Find the work done by F = -yi+ xj+ zk on a particle moving along the helix r(t) = where 0 < t <…

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Q: 5. For a vcctor Á written in spherical coordinates, A = A,f + A,® + AøØ, the spherical coordinate…

A: The answer is in below steps.

Q: Express the given parametrization in the form y = f(x) by eliminating the parameter. x = 5t + 2, y =…

A: Given

Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (c) Determine the…

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Q: Which of the following represents the arc length of the vector function r(t) = (sin 2t, e, ) on the…

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Q: Using an appropriate linearization, the local linear approximation of f(x) n+ cos a at is %3D

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Q: Q1: Consider the curve in E' parameterized by C:(t) = 1- Find the arc-length of the curve r(t)? 2-…

A: Given equation of the curve is rt=cos5t, sin5t, 12t

Q: 3. Find the arc length traced out by the endpoint of the vector-valued function 1 †(t) = t cos t î +…

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Q: 3. Sketch the space curve, r(t) = 8 cos ti +8 sin t j+tk , and find its length over the interval []…

A: Given: r(t)=8cost+8sint+tk    [0,pi/2]

Q: Q2. If ƒ = In(x² + y² +Z? ) then find the divergence of f also find its magnitude at (1,-2,3).

A: The given function is: f(x)=lnx2+y2+z2. Differentiate the given function with respect to x to obtain…

Q: - Evaluate the integral 4-z²-y² 1 dz dy dx Jo 4-z²-y² x² + y² + 2² using spherical coordinates.

A: To evaluate ∫-22∫04-x2∫-4-x2-y24-x2-y2 1x2+y2+z2 dzdydx

Q: au +20 dy 10 www ax dy dy?

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Q: .a. Compute the divergence of the function (V. v) v = (r? cos?0) î + (r² sin²e)ð + (r sin® cosø)

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Q: 13. Find the point on the curve 7(t) = (2 sin t, 2 cos t, t), 0<ts 7, where the tangent line is…

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Q: Suppose the divergence of the electric field in some spherical region is found to be V E = 5kr³.…

A: as given,   the divergence of electric field in some spherical region is ∇·E=5kr3 claim- to find the…

Q: (7) Let w(x, y, z) = xy cos z, where x = t,y = t², and arcsin(t). %3D dw Find dt

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Q: Q1- The divergence of the function f = (r5 cos 0)e, in spherical coordinates is.. .

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Q: Q1- The divergence of the function f (r5 cos 0)e, in spherical coordinates is...

A: The given problem is to find the divergence of the vector function in spherical coordinates.

Q: Use Linear approximation LCx) =f Ca)+fica) (x-a) to estimate he following quantities. Choo Se the…

A: 653

Q: Using an appropriate linearization, the local linear approximation of f(z)= T+ sin z at 27 is

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Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

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Q: .a. Compute the divergence of the function (V. v) v = (r² cos²0) î + (r² sin²0)@ + (r sin® cosø)@

A: Note: Since you have asked multiple questions, we will solve the first question. Please resubmit the…

Q: Find the divergence of the function * ? in spherical coordinates f = (r* sin 0)e,

A: Given information: Given function is  f = r4 sinθer

Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

A: First we have to find partial differentiation with respect to x , y and z of function f such that-

Q: Find the divergence and curl of F = (e¬* sin y , e¯Y sin z , e-² sin x). %3D

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Q: 2. Find the parametrization of the tangent line to the space curve r(t) = (-t3, In(t), e² ) at t =…

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Q: Given: vector-valued function R(t) whose derivative R' (t) = (4t, 6t, -12t) (b) Reparametrize R…

A: Let's reparameterize vector value function R(t).