(a) If F(v² – x²,v² – y², v² – z²) = 0 where v is a function of x, y,z show that 1 dv 1dv 1 dv 1 хдх уду z дz -- --

Q: 2x :S dr f(x, y) dy. f (x, y) dy. •1-x² f (x, y) dy. -V1-r

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Q: If f(x, y, z) = ln(xª + yl0 + 2³) + V (x10 + y8 + z4), then find fr, fy and f; at (1, 1, 1).

A: The given function is fx, y, z=lnx4+y10+z8+x10+y8+z4 and the given point is (1, 1, 1). Evaluate fx…

Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y = 2rsine

A: Here, the total derivative rule used is: z=f(x,y)=x2y2 & x=2rcos θ , y=2rsin θ

Q: Find fr, fy, and fz. f (x, Y, z) = z In(x°y²cos(52)) fa = fy = fz = ||

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Q: 9. Let f(x, y, z) = xyz=1 and r(t) = (e', t, t²). Find f(r(t)) at t = 1.

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Q: Suppose z = f(x, y), where f is differentiable, a = g(t), and y = h(t). If g(3) · fy( – 2, – 6) = –…

A: Find dz/st when t=3

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: 2. Let f(x, y, z) = In(x² + 2) + y²e#* - cos(2yz). Find fzyz-

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Q: 1. Consider the function f(x, y, z) = x² + 2y + 2², which is differentiable at (2,1,1). 1) find…

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

Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y=2rsinė

A: this is a problem of differential. Based on the general formula and concepts we will answer the…

Q: 3. Find the total differential of z = f(x, y) if z2 - y = (1– 2x)z.

A: Total differential of a function z=fx,y is dz=∂z∂xdx+∂z∂ydy

Q: Find the linearization L(X,Y) of the function  f(x,y)=y-1/x+1 at(0,0).

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Q: Let f(x, y, z) = x² sin y + y e², where x = t + 3,y = net-1 and z In 2t. %3D df at t 1 is: dt %3D…

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Q: Evaluate fSS 6e(²+y²+z²)/² dV over B where B= {(x, y, 2) : x² + y² + z² < 1}. Take T = 3.

A: Since we have    x2 + y2 + z2  expression in the integral and region B is the sphere of radius 1…

Q: 1. Let F(x, y) = 1 0 if x + 2y ≥ 1 if x + 2y < 1 Does F defines the DF in the plane?

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Q: 10. Find the linearization, L(x,y,z) of the function f (x, y, z) = e* + cos(y + z) at Po (0,",").

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Q: Find the linearization of the function f (x) = x at x = 1. a lal sin (a) L (x) Using this…

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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: w that the equation of the tangent space of f(x, y,z)=Vx² +y° +z* at point (2,3,4) is 1 K, y, z) =…

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Q: Let f(x, y) be differentiable at (ro, yo). Then we have f(xo + Ax, yo + Ay) - f(xo, y0) fa (ro, yo)…

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Q: Suppose f(x, y) =                             ((xy2) / (x2 + y4)), for (x, y) ≠ (0, 0)…

A: The given function is,

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: 4. Use the linearization of f(x, y) Vx + 2y to approximate f(3.01,2

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Q: If f(x) I (t° + 2t + 6) dt 0. then %3D = (x), ,f

A: The function needs to be integrated first and then to the subsequent function we will be double…

Q: Let F(x, y) = G , y 1 )- Calculate the work against F required to move an object from (1, 1) to (3,…

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Q: Suppose z = f(x, y), where f is differentiable, x = g(t), and y = h(t). If g(5) = 8, g'(5) = 9, h(5)…

A: Given that z=fx,y, where f is differentiable. Here, x=gt and y=ht. Also, let, g5=8, g'5=9, h5=-7,…

Q: 2. Find the linearization of the function f(x, y) = In(x³y®) at the point (xo, yo) (4, 3). Leave all…

A: Consider the following function: fx,y=lnx3y6 fxx,y=ddxlnx3y6=1x3y6×3x2y6=3x…

Q: Let f(x, y) = x² + In(2x – y). Find the gradient Vf(x, y) at the point (1, 1). O O O O

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Q: Assume that z = ƒ(x, y), x = g(t), y = h(t), ƒx(2, -1) = 3, and ƒy(2, -1) = -2. If g(0) = 2, h(0) =…

A: We use the partial derivatives to find dz/dt  Then plug x=g(t) and y=h(t)

Q: Suppose z = f(x, y), where f is differentiable, x = g(t), and y = h(t). If g(4) = – 4, g'(4) = 9,…

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Q: Show that the function no-f 0, z = 0 f(2) = { – y* z#0 x2 + y? x² + y² is not differentiable at z =…

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Q: Suppose that F(x,y, z) = 0 defines z as a function of x and y and F is differentiable. Prove that дх…

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Q: 2. Suppose that z = f (x, y) and both x and y are functions of a single variable t such that dy t2 –…

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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: Let f(x, y,z) = x² sin y + y e², where x = t + 3,y = net-1 and z = ln 2t. %3D df at t = 1 is: dt…

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Q: (a) Let f(r, y) = x - 3ry + 18y, where 3r?y- y- 6x = 0. Prove that f(r, y) has extrema at the points…

A: Calculate partial derivative of f(x,y) with respect to x and y ,

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: Suppose that z is a differentiable function of x and y with dz (1, 1) = 162 and(1, 1) = 6. dz ду dx…

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Q: (a, b), f (x, 42. Show that ifJ (2, Y) is differentiable at then the function of one variable J (2,…

A: Definition (Differentiability of two variable function): A real valued function f(x,y) is said to be…

Q: Assume x and y are functions of t. Evaluate dy for 4xy - 7x+4y3 = - 48, with the conditions dt dx =…

A: Explained below

Q: Show that f(z) = x³+i(1−y)³ is differentiable only at x = 0, y = 1 and f'(z) = 0.

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Q: Let m be a non-zero real parameter and f(x, y, z) = xy + mz2 cos(x) – 2xe32. Then the minimum rate…

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Q: Suppose that z = f(x, y) is differentiable at the point (64, 1024) withf, (64, 1024) = 3 and dz…

A: Topic:- partial derivative

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

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Q: prove that x^2y/(x^2+y^2) is not differentiable at 0,0 when  x^2y/(x^2+y^2) if (x,y) not equal to…

A: f(h,k)-f(0,0) =hfx(0,0) +kfy(0,0) +h2+k2∅(h,k) h2kh2+k2-0 =hA+kB+h2+k2ϕh,k ...(1) A =fx(0,0)…

Q: Suppose that z is a differentiable function of x and y with dz (8,7) = 80 and dx dz (8, 7) = 2. ду…

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Q: 2. Suppose that a function f: R3 → R³ defined by: f (х, у, 2) 3 (2х + Зу — z, sin(тхy?z-1),…

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Q: Consider the function: u = 2 ln /x² + y² Show that uzz + Uyy = 0. %3D

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