Find əzləx of z = tan-1(x²y) + tan¬1(xy2). v² dz dx 1+x*y?° 1+x*y* ху 4,2 2,,4 dz 2ху 2y? Əx " 1+x*y² * 1+x*yA əx 4,2 2,4 y? 2,4 1+x*y²°1+x?y* dz о дг 2y o əz 2ху 1+ x*y?°1+x?y* 4,2 2,4

Q: Use Green's Theorem to find f. [(2x – y+ 4) dx + (5y+ 3x – 6) dy] around a triangle in the xy plane…

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Q: In Exercises 61-68, compute the derivative indicated.

A: We have solved first three parts for you, if you want solution of other questions, repost them.…

Q: b) Show that F - dr is independent of its path, given that y F(r, y, 2) = 1+. + tan-2) i+ tanrj+ k.…

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Q: (b)Find the derivative of g in the direction of a= 2i+ curl w where at point (0,-1,1) g = In- 4 + 2…

A: Given, w=cosxyzi+xeyz+1j+xyzk Then, Curl…

Q: Consider the following IVP: у" +у'%3D-сos x;B у(0) %3D а, у(0) -b Find the general solution. A y (x)…

A: Solution of the differential equation

Q: (6,5,- 1) Evaluate the integral y dx +x dy +2 dz by finding parametric equations for the line…

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Q: dw Use the Chain Rule to find dt w = 7x°y°z,x = 2t, y = cos(4t), z = tsint %3D 7xy°(12yz -…

A: see 2nd and 3rd step.aa

Q: Show that the path given by r(t) = (cos t,cos(2t), sint) intersects the xy-plane infinitely many…

A: Consider the given path rt = cost , cos2t , sint  Then, xt=cost , yt=cos2t , zt=sint

Q: w In(x2 + y2 +z?), x = ue" sin u, y = ue" cos u and z ue", using chain rule at the point (u, v) =…

A: Given w=lnx2+y2+z2x=uevsinuy=uevcosuz=uev

Q: Let C = C₁ U C2 U C3, where C₁ is the line segment from (-1, −1) to (0, 0), C₂ is the line segment…

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Q: Find the differential dy: y = In(sec² ( 3ª²–20+5 312-2x+5 O (E) None of the choices dy = 2 (x – 1)…

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Q: (a) x = t* - t + 1, y = t2 Select--- v (b) x = 2 - 2t, y = VE --Select--- v (c) x = sin(2t), y =…

A: Match the graph with their parametric equations.

Q: (b) Find the derivative of g in the direction of a=2i+curl w at point (0,-1,1) where u u +2 g= In. J…

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Q: tan-i z = ÷In 1-ja sinh-1z = In(z + vz2 + 1) cosh-1 z = In(z + vz² – 1)

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Q: 2. Let F = 3.xyz i – 4xyz j + 2xyz k . Find div F and curl F. -

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Q: 1. Give an equation of the tangent plane to the surface z = In(4y – x) at the point (3,1,0). 2. Use…

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

Q: (1) (a) Show that the line integral tan(y) dr +x sec (y) dy is independent of path, where C is any…

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Q: A heart-shaped graph in a 2D plane is defined by the equation (x² + y² - 1)³= 4x²y³ Determine dy/dx…

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Q: Inz Vz Inz-z dz 2. Je cos 3r dz 13. S- ze-lal dz 74: cscz cot z dz dr dz dr 3/2 dz 26. J. v9-2 6.…

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Q: au %3D ax at u(x, 0) = 0 ди (x, 0) = 0 at u(0, t) = sin? t u(1, г) — 0,

A: Given,           ∂2u∂t2-∂2u∂x2=0                       for 0<x<1, t>0      ...(1)u(x,…

Q: Evaluate the line integral f (-y sin(xy)i – x sin(xy)j) dr using the potential function f(x, y) =…

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Q: x + y3 -1 Еxample If u = tan prove that x- y ôu ди (i) x. + y. sin 2u

A: # we are entitled to solve one question at a time , please resubmit the other if you wish to get it…

Q: 6. If V(x, y) = xsin x cos y + y² then, F-VV and it is equal to A. -ily sinx cos y sinx cos y]…

A: We can solve using divergence formula

Q: Two functions u and v of x and y are said to satisfy the Cauchy- Riemann equations if u, = v, and u,…

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Q: 9. Find all the second partial derivatives of Z; given: a) Z = xy°In(3xev) b) Z = Arctan ( x2 /y³)…

A: a) Given function is: z=xy3ln(3xey) Finding the partial derivative of 'x'…

Q: dt dx2 dy , ди u(0, у, 1) dx (1, y, t) = 0, и(х, 0, г) %3D ди - (х, 1, г) %3D 0, dx и(х, у, 0) %3D 2…

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Q: Use the Chain Rule to find az/ðs and ôz/dt. z = arcsin(x – y), x = s² + t?, y = 2 - 2st as az at II

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Q: sin(xz – 1) In(6+ 3xz + 4yz) = 0 determines z as function of x and y in a neighbourhood of the point…

A: Claim: at (x,y)=(1,1) for the equation  Take partial derivative with respect to x Substitute…

Q: a) Plot a direction field and some integral curves  for xy'-2y=-1 on the rectangular region {-1<or…

A: a) given differential equation  xy'-2y=-1 claim- plot a direction field and sole integral curves for…

Q: 1. Find of/ar, af/ay and of/0z (y- sin(x))² f(x, y) = (r - 1) (y+ 2) + S(1, y) = in(V + y²) + (z² +…

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Q: 9. Find all the second partial derivatives of Z; given: a) Z = xy In(3xe) b) Z = Arctan (x² /y®) %3D

A: Given functions for Z are: (a) Z=xy3ln3xey (b) Z=Arctanx2y3=tan-1x2y3. We have to find second order…

Q: rsin z cos t dt lim 2.r

A: Use L'Hospital rule and fundamental theorem of derivatives to solve it.

Q: Use Green's Theorem to evaluate the line integra Icon (y − x)dx + (2x − y)dy - - for the given path.…

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Q: The equations xe" + uz – cos(v) – 2 = 0 and ucos(y) + 6x²v – 4yz² – 1 = 0 can be solved for (u,v) as…

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Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = tan-1 (xyz) at…

A: To find the linearization Lx,y,z of the function fx,y,z=tan-1xyz at 1,0,0

Q: Represent f(x, y) (0<x < 4, 0 < y < 4) by a double Fourier series sin (). NTY f(x, y) = EEBmn Sin ()…

A: The given problem is to find the value of Bmn using double Fourier series with given f(x,y) series…

Q: Puestion 04: Use transform method to solve the following equation. Utt – Uxx = te¯*, 0 0 With the…

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Q: Let u(x,y,t)=(1/t)exp[-(x²+y²)/4t] where exp denotes e to a function. Show that u(x,y,t) satisfies…

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Q: In Exercises 23–26, find ƒx , ƒy , and ƒz . 23. ƒ(x, y, z) = e^-(x2+y2+z2) 24. ƒ(x, y, z) = e^(-xyz)…

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Q: find div and curl F F(x,y,z)= 7y3z2i- 8x2z5j-3xy4k F(x,y,z) = exyi-cosy j +sin2 z k

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Q: Solve the DEQ given the initial condition (4,-2). Graph it on the slope field. 10 9 1 8- Let…

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Q: Two waves on a string are given by the following functions: yı (x, 1) = 4 cos(20 – 30x) (cm) y2(x,…

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Q: (z - 1)dt + (1 – t)dz %3D

A: (4) Given differential equation is z−1dt+1−tdz=0......1. We have to determine the whether the…

Q: In this problem the arguments of sine and cosine are in radians. f(x, y) = cos(0.4x² + 0.8y?) COS a)…

A: Since multiple subparts are asked, we will solve the first three subparts only. To get the solutions…

Q: Find all the first partial derivatives of z = a sin 3y – 2y? cos 3x (Choose all applicable answers)…

A: Using partial derivatives.

Q: Find the total differential for the function w = 13z ysin x. dw = 13z ysin xdx-13z sin xdy-26z ysin…

A: Consider the function: Let,  w=13z3ysinx=fx,y,z The total differential of the function is given by…

Q: Solve: If A = i sin 2t + je3t + k(t³ – 4t) dA when t = 1. dt Find If F = x²yzi + xyz²j+ y°zk…

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Q: Let F(r, y, z) = (y² + 2z, 2ry + 4, 2a), and let the curve C be described by x = t, y = t, z = t3…

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Q: Find the first partial derivatives of 2х — 4у - f(x, y) = at the point (x, y) = (2,2). 2х + 4y af…

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Q: 4. f(z) = { |z|* z = 0 verify that the Cauchy-Riemann equations are satisfied at the origin z =(0,0)…

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