In Exercises 23–25, find ƒx , ƒy , and ƒz . 23. ƒ(x, y, z) = x - 2y2 + z2 24. ƒ(x, y, z) = (x2 + y2 + z2)^(-1/2) 25. ƒ(x, y, z) = sin-1 (xyz)

Q: 3.2.10 Example: By method of contour integration, prove that dx = t /4 (1+ x }

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Q: Compute div F, where F(x, y, z) = (x² + 3y, y? – 4z, sin r cos y – 22). A. (4 – sin r sin y, – cos r…

A: Given : F(x, y, z)=(x²  + 3y ,  y² -4z ,  sin(x )cos(y) - z2 )  Now we find div F = ?

Q: Find Vf at the given point. f(x, y, z) = 32³ – 2(x² + y²) z + tan '(4xz), (0, 2, 3) Vf\(0,2,3) f(x,…

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Q: 4. Let f(x, y) = 2TY x = In 2 g and y = In s. . a. Find the equation of the tangent plane to f(x, y)…

A: Let f(x,y)= 2xy , x=t/ln2 and y= lns Here we have to find the equation of the tangent plane to…

Q: Answer: y = (2/x) + (c/x)ex

A: Given

Q: Find the maximum and minimum values attained by f (x,y, z) = xyz on the unit ball ² + y² + z² < 1.

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Q: Express a general solution to 2x(1 – x)y" + (3 – 10x)y' – 6y = 0 Using Gaussian hypergeometric…

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Q: 8. Find the flux of F = (2x – 5y², 3y, x) out of the sphcre of radius 2 centered at the origin.

A: The flux of the vector space is given by the formula, ∫S∇.F dS where S is the sphere of radius 2…

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: 21 (important) Find the fixed point for F(x) = ax + s. When is it attracting?

A: Given Fx=ax+s

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

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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: 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: azz 2. A. If z = sin(3x+2y) , verify that 2 - 3 a2z = -6z ay2 B. If f = x³y³ + 2xcosy + y² lnx then…

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Q: 36. Using the approximation dy dy h dr * Yn+1- y. and that dr 1, y = 2 when r 0. Then, y A h- 2 h+ 2…

A: Please see the answer below.

Q: 2. Show that the Euler-Cauchy Equation Iy" + axy + by = 0, 1+0 can be transformed into the constant…

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Q: t, 01 1 a.) f(t) [m (sh w + (cos w - 1)] cos wt + [[ -[sin sin OLL - cos w + sh w]]sin wet dw - 1…

A: Given the function is ft=t0&lt;t&lt;10t&lt;0, t&gt;1

Q: f(x, y, z, w) = (1+x+ sin(z − 2y), ez-w, 2z+tan(w+x²)).

A: we have to find the approximation of ƒ at the point P = (0, 0, 0, 0).  For this we use the proper…

Q: 4. Curl of f (x, Y, z) = 2xyi + (x² + z²)j + 2zyk is

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Q: (4,0,2) S sin y cos x dx + cos y sin x dy + 3 dz (1,0,0)

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Q: aーメ ターメ2.y to い-X to cylindHcal coordin ates

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Q: The second order homogeneous Cauchy-Euler equation defined by: 2d²y +bx- dy ォマ +cy=0 dx2 dx (ay"…

A: We have to choose the correct answer

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: Double integrate under z=xy, above the triangle with vertices (0,1),(0,4),(1,1).

A: We have to find the volume by double integration

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: Find the potential function for F(x,y,z) = (x^-1z)i + (y^-1z)j + ln(xy)k. Show all steps and explain

A: Potential function of  F, is f such that ∇f=F.

Q: Find the Second appoximation for the System. X Sin y at (xo,,)= (1, 1). y=Cosx

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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: 1.6 Evaluate the line integral f x*dx + xydx where C is the triangle with vertices at (0, 0), (0,…

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Q: 2. Prove that the directional derivative of f(x, y, 2) = ry sin z at (1,2, ) in the direction v = i+…

A: Given:        fx,y,z=xy sinz         x,y,z=1,2,π2    direction v=i+2j+2k   Differentiate the…

Q: Show that sin(y) 2e-" sin(x)) + ( .cos(y) + 2e¬#cos(x), 2)e/ = 0 %3D is not exact but becomes exact…

A: We have to solve given problem:

Q: 6. Let z = 5e** sin y . Compute the differential dz. A) dz = 20et* sin y dx + 20e** cos y dy B) dz =…

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Q: Determine the type of points on the x(u, v) = (u, v, u²) surface. Differential geometry

A: Given point is Xu,v=u,v,u2.  This point is of the form Xu,v=fu,v,gu Let Xu,v=xi+yj+zk. Then,  x=u…

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: 26. y = sinh x, y= e, x = 0, x= 2 27. y = Vx, y =;x, x= 9 28. y =x, y = 2.x², x + y = 3, x>0 II

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Q: Vhat is the general solution of (x + y) dx + tan ady O xsinx + cos x + ysinx = C O sinx + y cos a +…

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Q: Determine if F=(e* cos y + yz)i + (xz-e* siny) j+(xy+z)k is conservative. If it is conservative,…

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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: Find div (e" grad u x 7) u=x-y ex at (2,1,0) where and =(x²+1)i + sec¯¹(x² −y)j + 3y²zk

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Q: Explain, the given differential 3x²dx + 2yz dy + y² dz is exact or not.

A: We will check whether  3x^2dx+2yzdy+y^2dz is exact or not.

Q: Differentiate: y = 2sinx/e O a. y' = (cos x- sin x)/e O b. y = (2e*cosx - 2e*sinx)/e2x O c. y…

A: Please see the solution below.

Q: 1 find the total differential dz. z=xsin y + x² z = (2x² + 3y)² z=5x-7y

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Q: 10. Find the work done by the force F=vx +2y y - 7 for a particle that moves between points (-1,0,1)…

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Q: 6. Find S(3y – y³) (1– y?)dy sin ycos y 7. Integrate: J sin² y dy 8. Find 3 S(5 - 3y-5)²dy

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Q: In Exercises 23–25, find ƒx , ƒy , and ƒz . 23. ƒ(x, y, z) = sec-1 (x + yz) 24. ƒ(x, y, z) = ln (x +…

A: We’ll answer the 23rd question since we answer only one question at a time. Please submit a new…

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

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