Find fr and fy for f(x,y) = I+y fz = /(r+y)? and fy = /(r+y)2

Q: Find fy (x, y) for f(x,y) ry

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Q: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

A: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

Q: 3. Find fz and fy where f(x,y) = In(x + y²).

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Q: What is the directional derivative of f(x, y, z) = bx²y²z² + x² + y² + z² in the direction of v =…

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Q: a) Find the directional derivative of f(x, y, z) = x²yz + 4xz² at (1, -2, 1) in the direction 2i - j…

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Q: solve the differenhal equa hon by varianon of parameters y" + 3y't 2y 7 te* y (x)

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Q: 2. If F(x, y, z) = 2z3 – 3(x² + y²)z, then verify that Frx + Fyy + F2 = 0. %3D

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Q: 3. S sec z tan z dz 2 2

A: Given: 3.∫sec23z tan23zdz

Q: Find fr, fy, and fz. f(r, y, 2) — вуzIn(4ry) fz fy f: =

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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: Find fz(x,y) and fy(x, y) given f(r, y) = csc yArcsin(r²).

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Q: Solve ux – uy +yu = 0, where u is a function of x and y. %3D

A: Given: ux-uy+yu=0. The objective is to solve u, where u is a function of x and y.

Q: 2. Find frxz for f(x, y,z)= z² e³xy

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Q: Let { sin(r-y) |r|+ |y| 0 (x, y) = (0,0) f(x, y) = Is f continues at the origin? Why?

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Q: Find the linearization of the function f(x, y) = /36 – læ² – 2y² at the point (3, -1). L(x, y) = Use…

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Q: Find the maximum rate of change of f (x, y) = xln /x2 + y2 at (1,2) and direction in which it…

A: To find the maximum rate of change of fx,y=xlnx2+y2 at 1,2 and direction in which it occurs.  First,…

Q: Consider the function f(x) = 3z10 + 3z° – 3z² – 4. Enter the general antiderivative of f(z)

A: Given function is : f(x)=3x10+3x5-3x2-4 We have to find antiderivative(integral) of the given…

Q: Evaluate f, xyz dV, where Q = {(x, y, z): 0 < x < 2y, 0 <y< 1, 0 < z < x+y}.

A: According to question,Q = x,y,z : 0 &lt; x &lt; 2y, 0 &lt; y &lt; 1, 0 &lt; z  &lt; x+y

Q: Find the linearization of the function a) z = cos(sin y – x); at (-2,0) and use it to approximate…

A: Suppose f(x,y) be a differentiable function at (a,b). Then linearization of f(x,y) at (a,b) is given…

Q: Find fzyz. f (x, y, z) = x°y°z° + xy7 + y®z f zyz ||

A: Using derivative,

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

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Q: Find the derivative of the function f(x,y,z) = x² + 2y? – 3z2 at the point v =. Po = (1,1,1) in the…

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Q: Determine the value of fr at (1, – 1) when f(x, y) = 3x + 2xy? – 2x²y + 4x.

A: Our Aim is to determine the value of fx at (1,-1) whenf(x,y)=3x3+2xy2-2x2y+4x -(i)

Q: Using the linear approximation of f (x, y) near (x, y) = (1, 0) tells us that f (0.98, 0.05) is…

A: The linear approximation of a function f(x, y) at (a, b) is L(x, y) = f(a, b) + fx(a, b)(x − a) +…

Q: How much work is done by a variable force F(x) = 7/x  N that moves an object along a straight line…

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Q: A particle is moved along the x-axis by a force F(x) = x² + 5x – 6 . How much work is done in moving…

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Q: Find fr, fy and fz. f(x, y, z) = x – Vy² + z? |

A: Given f(x,y,z)=x-y2+z2. The objective is to find fx,fy and fz.

Q: Find fr and fy- f(x, y) = 7e dt f-(x, y) = f,(x, y) =

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Q: In integrating the function fx* in Sx dx using integration by parts, what would you choose for your…

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Q: Find fr and fy- f (x, y): 6e dt 4 fa(x, y) = fy(x, y) =

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Q: Integrate the function f (z) = (z – 8i)² from z = 0 to z = 4 + 4i along the line x = y. 2

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Q: 12. Find frxyz for f (x, y, z) = sin (3x + yz)

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Q: - x'yt, show that fxy = fyx. 7,4 Given f(x, y) = et*

A: Given f(x,y) = e(x^4y^9) - x7y4

Q: ||| V3(x² + y²)dV, where V is bounded by y = 2x² + 2z² and y = 8.

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Q: Find fyxy. f (x, y) = x"y® – 20°y +x f yay YxY

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Q: Use the Trapezoidal Rule with n = 4 to estimate f, (x³ + 1)dx.

A: We have to estimate ∫-11x3+1dx by using the Trapezoidal rule with n = 4.

Q: Find fr, fy, and fz. f(x, Y, z) = 4yz In(6ry) fz = fy = f: =

A: Given: f(x, y, z)=4yz ln(6xy)

Q: Find fyy for f(x, y) = e* In(y).

A: The given function is fx,y=exlny.

Q: How much work is done by a variable force F(x) = (60 − x) N that moves an object along a straight…

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Q: Find fr and fy- f (x, y) = | 5e dt %3| fa(x, y) = fy(x, y) =

A: We apply fundamental theorem of calculas and solve it.

Q: The gradient of f(x, y) = xy at (x, y) = (3, 1) is

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Q: Find the differential of f(x, y) = 3+y² at the point (2, 3). df: ((3x^2)dx+(2y)dy)/(2sqrt(x^3+y^2))…

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Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 7y + 3z) at the point (– 2, – 3, – 6). - -

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Q: What is dufferential equation of x'=4x-y and y'=-4x+4y when t=0, x(0)=1 and y(0)=1

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Q: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

A: See the attachment

Q: Find f-(x, y) and fy(x, y). f(1, y) = (y^tan(4x)) fa(x, y) : fo(x, y)

A: The given function is: f(x,y)=y5 tan(4x)-43

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

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Q: Calculate fz(2, 3, 1), where f(x, y, z) = xyz.

A: Given,          fx,y,z=xyz

Q: 4) f(x,y) =Vx +y Ans. f.= +y Vx + y?

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