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

Q: Let f(x, y) = In( + 2y² – xy). Find fæz, fyy, fzy, fya. Confirm that fry = fya.

A: Given: f(x, y)=lnx2+2y2-xy. To find: fxx, fyy, fxy, fyx.  And to show that fxy=fyx. Differentiate…

Q: Q2/ Prove that 1 dx = v2 Jo 1+sin(x)

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Q: The function f(z) =e² is: u(x.y)=e*cos(y) o u(x,y) =e*sin(y) ¤ contiuous in СО discontiuous in CO

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Q: Evaluate the iterated integral " SL* x² sin y dy dz dx .

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Q: Let f(x,y, z) = xtan (Vyz)- sin(e*) , evaluate zy %3D дудхда

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Q: fyx if f(x, y) = sin(xy) + x² In y cos(xy)- xysin(xy) - cos(xy) + xysin(xy) + cos(xy) – xysin(xy) +…

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Q: Suppose that z = xy² and x and y are differentiable functions of t with x = 1, y = −1, dx/dt = −2,…

A: Given  z=xy2 Also at t=-1 x=1y=-1dxdt=-2dydt=3

Q: Use linear approximation to find y = L (x) of the function f (x) = = COS X about the point xXo = JT…

A: Use formula of  linear approximation

Q: Find and by implicit differentiation, and confirm that the - dy results obtained agree with those…

A: The solution is as follows

Q: Use Green's Theorem to evaluate the line integral. ex cos(2y) dx – 2ex sin(2y) dy C: x2 + y2 = a²

A: Use Green's theorem

Q: Let f(x, y) = x sin ry. Find: fyy (x, y) fyz(x, y)

A: f(x,y)=xsinxyfx=sinxy+xycosxyfyx=xcosxy+x(cosxy-xysinxy)=2xcosxy-x2ysinxyfy=x2cosxyfyy=-x3sinxy

Q: Let v(x, y) = cos(4x)sinh(4y). Find f(z)with Im(f(z)) = v(x, y). I

A: Given function is v(x,y)

Q: Let y(t) be the solution of dy/dt= 0.3y(2 − y) with y(0) = 1. Determine lim t→∞y(t) without solving…

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Q: Calculate $o (3x + 5y - cos(y)) dx + x sin(y) dy if C encloses a region of area 4.

A: To evaluate the given integral.

Q: Find f. fy for f(x,y) = xcosy + %3D x5 siny3 ey

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Q: 4. If f is a differentiable function of a and y with w f(x, y), x =r cos 0 and y = r sin 0, %3D show…

A: To verify the given relations between partial derivatives.

Q: Let f(x, y, z) = ln(x² + z) + y²e®z – cos(2yz). Find fzyn. Zyx ·

A: Given function is  f(x, y, z)=ln(x2+z)+y2exz-cos(2yz)

Q: Let Z = In X - y dz Find and dx dz dy

A: I have given the answer in the next step. Hope you understand that

Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

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Q: Find the total differential of the following: 1. f(x, y,z) =-tan'(x + y +z)+ In(xyz)

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Q: Evaluate the integral (1+ sin t)' cos t dt using the substitution u = 1+ sin t. (1+ sin t)' cos t dt…

A: Recall: ∫xndx=xn+1n+1+C

Q: Let F(x, y, z) = z* +x+y sin x +x In z 0, where z =f(x, y), then at (0,0,1) and %3D are equal to:

A: Given,          Fx,y,z=z4+x+ysinx+xlnz=0 , where z=fx,y

Q: Evaluate the iterated integral 2y dy dx 2 x +1

A: on solving this we get the

Q: tion z2 – (x2 + y2)2 and let p = (0, 0, 0). ermine the set Tp(Zf ) of all tangent prs to Zf at p. Is…

A: Sol

Q: Let f(x, y, z) = ln(x2 + z) + y2exz − cos(2yz). Find fzyx.

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Q: (a) If f(x,y) = e" siny – e sinx then verify that fæy = fyx. %3D -

A: Given that  f(x,y)=e^xsiny-e^ysinx To verify the fxy=fyx

Q: Let z = In(x² + y²) be a differentiable function of x and y, where x = sin t, y = cos t. dz when t =…

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Q: If z is a function of r and y implicitly defined by dz Əz find and dr ду at (x, y, z) = (0, 2, -1).…

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Q: Let v(x, y) = cos(4x) sinh(4y). Find f(z)with Im(f(z)) =v(x, y).

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Q: Use Simpson's Rule e with n=10 Y: X Sin (x), OSXS 27

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Q: Evaluate the iterated double integral: x+4 sin (y – 3y?) dy d.x x+4

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Q: 2. Let L:= D2 - x-D+4x2. Verify that Ly 0 where y(x) = sin(x). %3D %3D %3D

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Q: 3) Find if w = 5 cos(xy) – sin(xy), x = ,y = t,z = t³ %3D dt

A: Let's find.

Q: Given that y + x + cos(xy) = 0. Show that dy/dx = ysin(xy)-1 /1-xsin(xy)

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Q: he tangent plane to the function f (x, y) = cosh x + cos(ny) + e*+1)y at the point (0, 1, f(0, 1))…

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Q: Assume x and y are functions of t. Evaluate dy / dt for the following. y3 = 2x 4 + 6 ;        dx /…

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Q: Let f (x,y) = sin(xy) + x² ln(y). fyx at (0,) is equal to: %3D А. 33 В. О С. 3 D. 1

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Q: if wa2ey-Inz find dw dt X=In (t*, 1) y=tant 2set

A: According to power rule of differentiation and according to product rule of differentiation . Also…

Q: Find a potential function for F(x, y, z) = (y² cos z, 2xy cos z, –ry² sin z). %3D COS

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Q: %3D a) Find fyxyx for f(x,y) = In(xy) – cos (xy) at (1,t).

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Q: Differentiate implicitly to find Zx, Zy, and zxx, given: Z = xy' – sin( yz)

A: Given function is z=xy3--sinyz To find zx, zy and zxx. Solution: Implicit differentiation means…

Q: Let Juce) 2ntv () %3D A=O n!F (I+u+n) Bessel function Of the first Kind be a Of Order V Show that…

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Q: Find the total differential of the following: 1. f(x, y) = sin x+ ye 2. f(x, y, 2) = – tan"(x+ y+ z)…

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Q: Find of /dy if f(x, y) = y sin(xy) 1 + xycos(xy)csc(xy) csc(xy) B) xy cos(xy) + sin(x) A) O

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Q: dydx tan x 1. 1+ y²

A: We need to calculate double integral in given order dydx   we use result of inverse Trigonometry…

Q: Evaluate [xy dx+(x+y)dy along the curve y=x² from (−1,1) to (2,4). [Verify using Mathematica]

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Q: Find the general sebution of the oDE dy Sin(x+y)+ Cos (X+y) %3D dx

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Q: Assume x and y are functions of t. Evaluate dy over dt for the following. y = 2x 2 + 6 ; dx over dt…

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Q: Show that the function f(x,y) =x² cos² y+ ysin² x+xe" , satisfies the 2 COS Lipschitz condition in…

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