10. Given f 3D (x'y. уг3, -2:3x), find а) сurl F b) div F

Q: 10. If z = x + f(u), where u = xy, show that dz = x. х дх

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Q: 1. Use an antiderivative to show that for every contour C extending from a point z₁ to a point 22, 1…

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Q: Find ôf af of and дх ду dz f(x, y, z) = 3×EYZ + 7yexz af -7 Əx af 7 ду af 3xe"y + 7yex %3D X ze

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Q: Find fx, fy and f z if f(x, y, z) = e*yz In zx. %3D

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Q: Find the domain and range of:

A: (a) We know that the domain of the square root function is always greater than equal to 0. Thus,…

Q: (c(2z+y), %3D ue of c in the joi F of W.

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Q: if y = secx prove that y^2+y=2y^3

A: Equation relates the number of variables combined together by algebraic entities using equality…

Q: Suppose that z = f(x, y) is differentiable at the point (1024, 64) withf, (1024, 64) = 4 and f,…

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Q: Determine la derivada direccional de f (x, y) = y In z en el punto P (1, 4) en la dirección de v = i…

A: Topic:- calculus

Q: Suppose that z = f(x, y) is differentiable at the point (1024, 256) withf(1024, 256) = 2 and f,…

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Q: Aşağıdaki alıştırmalarda, f., fy ve fiyi bulun. 23. f(x, y, z) = 1 + xy² – 2z2 25. f(x, y, z) = x -…

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Q: dv av and ду ди ди 2. suppose f(z) = u(x,y) + iv(x, y), show that əx %3D ду əx ||

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Q: Determine (x, y) and 2(x, y), where f(x, y) = X sen(xy) %3D y

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Q: 5. Given that f (x, y) = sin y, determine fy(x, y).

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Q: Let x,(t)-v(t)+sin(r), x,-vt) then x,(t)= xN-cosit) Select ones True, False

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Q: A If w= f (x, y), where x = rcos 0 and y = rsin 0 , show that 2 1 + 2 +

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Q: Show that f(x,y)=exyx is differentiable at point (1,0) using the definition of differentiability.

A: A function is called differentiable, if the derivative of function exists at each and every point in…

Q: 49. If f(u, v, w) is differentiable and u = x – y, v = y – z, and w = z – x, show that af af ду af…

A: Given f(u,v,w) is differentiable. By chain rule of differentiation , we have

Q: Suppose that z = f(a, y) is differentiable at the point (1024, 1024) with, (1024, 1024) = 5…

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Q: 10. If z = x + f(u), where u = xy, show that дz dz х дх = x. ду

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Q: Find f, and f, for f(x,y)=y In (2x+7y).

A: F(x,y) = y ln(2x + 7y) To find : fx and fy

Q: Find Duf at P. 1 2. f (x, y, z) = 6x³y°z°; P(2, – 2, 2); u %3D - -

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Q: Find the -of the following function : ду w = cos (x2 + 2 y) – e4x- z*y + y3 .A a w = 2 sin ( x2 + 2…

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Q: Show that u is s is mmomphie to F' Lt T:VaV (V is as abore let Tuct) zt u'Le) 2 the derivative im…

A: Let F=ℝ and V=a+bx2+cx4 :a,b,c∈ℝ . Show that V is isomorphic to F 3. Let T: V→V defined as follows,…

Q: Given f(x, y, z) = /2x – y – 5z, find - - f-(x, Y, z) = %3D f,(x, Y, 2) = %3D f-(x, Y, z) =

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Q: Let f(x, y) = xcosy - ye*y. fry at (1,0)is equal to: -1

A: See the attachment

Q: Let f(z)=ex^2 = U(x,y)+iV(x,y) Verify Ux=Vy

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Q: Compute F. dr where F (x, y) : (7xy + x cos x) i+ (-yev + 6x²) j and C is a piecewise closed curve…

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Q: Q2:show that the force Fexyzi-x4z'k is Conservative. ?

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Q: Suppose that z = f(x, y) is differentiable at the point (1024, 1024) with f,(1024, 1024) = 5 andf,…

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Q: Given f(z, y, z) = /1z2 + 3y? + 222, find %3D f-(z, y, 2) =| f,(z, y, 2) = f.(z, y, z) =

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Q: Show that the function u = p(xy) + Vry v(y/x) provides the quation = 0. dy?

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Q: Let f(x,y) = xcosy – ye*y. fry at (1,0)is equal to: -1 -5

A: fx is partial derivative with respect to x fy is partial derivative with respect to y

Q: is function oF x $ y xz + y In x = ze-sin (xy) D. Ausumo that z Find zx iF

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Q: Suppose Vf(x, y, z) = 2xyzexi + zex¯j + yex k. If f(0, 0, 0) = 1, find f(1, 3, 3). ,2 .2

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Q: 3. Find and at (0,0) where if (r, y) # (0,0) if (z, y) = (0,0) f(1, y) = Are they equal?

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Q: T= tanh (x+ 2y+ 3Z) %3D finds O Tyy @ Tyx 3 Txy Tz Tzz Tzx @ Tzy

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Q: Suppose that z = f(x,y), find for 4 x²z* – 5yz³ + xy? - 3z? = x

A: Given: 4x2z4−5yz3+xy2−3z2=xz=f(x,y)∂z∂x=?

Q: Suppose f is differentiable at (3, 4), V f(3, 4) = (-V3, 1), /V3 and u = Compute D„f(3, 4). 2

A: ∇f3, 4=-3, 1, u=32, -12

Q: Show that the function u = 9(ry) + /TY v(y/x) provides the uation ‚²u y? 0. dy?

A: First find the partial derivative of the given function with  respect to x :

Q: Show that if |sin z| is bounded along the straight line {(x, y) : ax - By = 0}, then a = 0, i.e.,…

A: We know, sin z = sin x cosh y + i cos x sinh y, Where, cosh and sinh are hyperbolic functions.

Q: Consider f (x, y) = re63ry f-(x, y) = e63ry and fy(x, y) = %3D e63ry

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Q: f (x, y, 2) = x³ /+42³y² – xyz +x² – Vz5 VI+ 42°y? – ryz+ x² – Vz5 - -

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Q: xyz f(x.y.z) = et ot function is given P(2,,4) in point fux + fyy + fzz colculate.

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Q: Given that f(r, y) = }2 - - . (a) Calculate: f,, (b) Calculate: f„, (c) Are they equal?

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Q: me succe LO SUIVE uie folnoWing 2 и (х)— | (x -t )u (t )dt 2 --

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Q: f(x, y) = /32² + 3y fz(4, 5) = VT23 %3D

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Q: Use the linear approximation to ƒ(x, y) 12x² at (3, 9) to estimate f(3.1, 8.8). y2+7 (Use decimal…

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