Find fæ, fy, and fz. 4,5 f(x, y, 2) = 4z In (a*y° cos(5z))

Q: Q1// B: If u+v=e cos y and u-v=e'sin yfind the Jacobain of the a u, v at (x.y) (1,0) dx,y function

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Q: w = x Tan (yz), x = u2, y = e2v , z = v cos u. Find wu and wv 10.

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Q: 2: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G(x, y) = x³y² + y² sin…

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Q: 2. f(x, y) = e' cos y; P(0, 1/4); a 5i-2j %3D %3D

A: Given the function  f(x, y) = ex cos y   at  P0, π4 and  a = 5i - 2j To find the directional…

Q: r(t) = cos(at)i ln(t)j + √t − 4k; to = 5 2 ms of i, j, and k. Domain is: (, ) NOTE: Enter r(5) ||…

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Q: 4. y = c, sin wt + c, cos wt w is a parameter

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Q: r(t) =(sin 3t, cos 31, V7t), 1. Let a) Find T(t) and N(t)

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Q: Find T(t) and N(t) at the given point. x = e' cos t, y = e' sin t, z = e'; t= 0 T(0) : N(0) =

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Q: Solve for C using the form f(x,y)=C. Given [2x + ycos(xy)] dx + x cos(xy)dy = 0; f(1)=pi/6. 1…

A: We use the concept of exact differential equations to find the general solution to given…

Q: Q.5 If P=r cos t and rsin t-2te = 0, find dP/dt.

A: Given ,  P = r cost and r sint - 2ter = 0 We have to find dP/dt Since ,  P = r cost  Then ,

Q: Inx Q1// B :- If u+v=e™ cos y and u- y=e*sin yfind the Jacobain of the alu, v) function a x, y at…

A: We have to find the Jacobian of the function ∂u, v∂x, y at the point x, y=1, 0 where u and v are…

Q: and y = - V 8) Let ze, where x = √uv and Find dz dy in terms of u and v.

A: Given: z=ex2y x=uv y=1v To find dzdv in terms of u and v

Q: y" – 5y' + 6y = 10e' cos t, y(0) = 2, y'(0) = 1 %3D

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Q: Given z = 2 cos t + 35 and y= 9 sin? t da (i) dt dy (ii)- dt dy (iii) dx

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Q: Find fa, fy, and fz. f (x, y, z) = 3z In (x*yt cos(2)) 4,4 fm = fu f2 =

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Q: Find T(t) and N(t) at the given point. x = e' cos t, y = e' sin t, z = e'; t=0 T(0) = N(0)

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Q: 16. y' + (2/t)y = (cos t)/t, y(n) 3D0, t> 0

A: The given DE is: y'+2ty=costt2

Q: dy Os:A- Find for the following functions: - dx 1- 1+secy xy2 = 1+ x* t2 2- If y = and t = V2x + 1…

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

Q: dz dz and dv Use an appropriate form of the chain rule to find du z = =; x = 16 cos u, y = 15 sin v…

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Q: If f(z, y) = e" sin(4y) then: V f( – 1, 1) =

A: Given function is f(x, y) =e4xsin4y.  We have to find ∇f(1, -1 ). The vector differential operator ∇…

Q: f f(2) = / cos(t) dt, then f'(x) = %3D COS Select one: a. 3e cos(a?) b. e cos(ez) c. 3e cos(e6z) d.e…

A: Given : fx = ∫1e3xcost2dt

Q: H.W: find dz and əz | ди ὃν z = 4e* ln y, x = ln(u cos v), y = u sin v as functions of u and vif:

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Q: at (s, t) = (0, 1) if ds z = 6x + y² tan (), x = e" – st, y = s² – f.

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Q: alu,v at dx,yl Q2// B :- If u+v=e"cos y and u- v=e" sin y find the Jacobain of the function (х,у)…

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Q: Find the value of dʻy/dx at the point defined by the given value of t. x = 5 sin t, y = 5 cos t, t=…

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Q: C) Find a z and of xy" ay (xy2) - -군3 COs %3D

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Q: 2. f(x, y) = sin(xy) + x² In(y) Find fx at (0, "½) a) 33 b) 0 c) 3 d) 1 +)

A: Given , f(x,y)= sin(xy)+x2ln(y) we have to find fyx at (0,π2)

Q: Q5/ Find Vf for f(x, y, z) = e** cos z +(y+ 1) sin-x at the point (0,0, T/6)

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Q: N 1 1 202 2{(xn – µ)²}– z(Ord – r). n=1

A: Let y be a function of x and if a is a constant, then we know that ddx(a-x)2= -2(a-x). Here, we need…

Q: .3 *csy +a Sina, If f(x,y) = e which of the following is Correct ? A. fa(Z,4) = e*(o54+3x? Sinstaš…

A: differentiate partially with respect to x and y respectively.

Q: Find D (x, y, z) where f(x, y, z) = cos(z²)sin(y²) In the direction of v = (4, 15, 18). %3D Possible…

A: Introduction: The formula for the directional derivative of the function f(x,y,z) in the direction…

Q: S(z, y, 2) = 122 y sin(z) – Vy- z cos(r+y) 8PR Find Vf.

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Q: 31. f(x, y) = e cos y a. (0, 0), b. (0, п/2) %3D at

A: We know that linearization of f(x,y) at (a,b) is

Q: Q1: Find the length of the cardioid r= 1 + cos 0 0 < 0 <T

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: a²z + ax? (c) Show that the function z = e* sin y + e cos x satisfies Laplace equation a²z = 0. ду?

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

Q: (c) Show that the function z = e* sin y + ev cos x satisfies Laplace equation ax? a2z = 0.

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Q: If u = x3 + y3 where x = a cos t, y = b sin t, then du dt

A: Solution

Q: Question 9

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Q: . и., — и. — sin x сos t, t>0 В.С.: и(0, г) %3D0, 1.С.: и(х, 0) %3D 0, 1,(x. 0) = 0

A: Solution :-

Q: • T/4 cos(0) f |/| f(x, y, z) dV = 9p sin(ø) cos(4) dp d0 dø, find f(x, y, z). E f(x, y, z) =|| ?

A: We have to given ∫∫∫Efx,y,zdV=∫0π2∫0π4∫0cosθ9ρ2sinϕcosϕdρ dθ dϕ Now the function which is to be…

Q: 9. Jer'y ds, C:x cos t, y sin 1, z = 1, 0<1s/2 %3D 77

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Q: T/2 %3D cos (2wt + O, + ©z)dt = 0 -/2

A: The solution are next step is

Q: 4. r(t) = (cos t)i + (sin t)j + (sin 2t)k, t, 2 %3D

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Q: rz cos 0 12. Let F(r, 0, z) = rz sin 0 (а) Find F'. (b) Find det(F').

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Q: Find T(t) and N(t) at the given point. x = e' cos t, y = e' sin t, z = e'; t= 0 T(0) N(0) =

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Q: Find fa, fy, and fz. f(x, y, z) = 3z ln (x³y³ cos(2z)) fx= fy= f₂ = =

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Q: 5. Find Sp√x² + y² dr, where ř(t) = t cos t tsint Ost), 0 ≤t≤ 2π.

A: Given r→(t)=tcosttsint,0≤t≤2π. The objective is to find ∫Px2+y2dr.

Q: 6. Let r = t sin t, y = t cos t, 0<t<1. dy (a) Find dr

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Q: By about how much will h(x, y, z) = cos (paixy) + xz2 change if the point P(x, y, z) moves from…

A: The given function is,