Evaluate fcF. dr where F = ( 3 z – y)i + (2 x +2 z)j + 2 z k along the straight line from (1,1,2) to (2,2,1)

Q: Example: Calculate the value of (@w/0x) at the point (x, y, z) = (2, -1,1) if:- w = x2 + y2 + z? z3…

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Q: Find the best-fit quadratic function f(t) = co+ c¡t + czť² to the data points (0, 7), (1, 6), (2,…

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Q: Find the exact value of Duf(-2,-1,-3) in the direction of v = 3i+ 4j + 5k for the function f(x,y, z)…

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Q: Find the linearization L(x,y) of the function at each point. f(x,y) = x² + y² + 1 a. (4,1) b. (1,1)

A: To find the linearization Lx, y of the given function at each point.fx, y=x2+y2+1 a 4, 1b 1, 1

Q: Find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously f(x, y) = x2 − xy…

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Q: Find the minimum and maximum values of the function f(z,y, z) = 3r # 2y + 4zsubject to the constramt…

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Q: Find the linearization L (x, y) of the function f (x, y) = y/-x at (-9,4). 2 L(x, y) -x+ 3y – 6 3…

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Q: If Z = x.n. f .f (**²), then show that: X. Zx + y.Zy = y

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Q: 3. Classify the stationary points of (a) f(r, y, z) = x² +x*y+y'z+z7-4 (b) /(.x2, X, r)- 20xy +48r,…

A: Given function is fx1,x2,x3,x4=20x2+48x3+6x4+8x1x2-4x12-12x32-x42-4x23           (i) To classify the…

Q: o Find the Vf at the given point 1.f (x,y,2)=x² + y² -2:2 +z In x,P(1,1,1)

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Q: assume thatf (2, 3) = 8, fx (2, 3) = 5, fy (2, 3) = 7 Which of (a)–(b) is the linearization of f at…

A: Consider the given: f2,3=8fx2,3=5,fy2,3=7,

Q: Show that the function u(x,t) = t/2e-*/4 (t > 0) satisfies u, = uxx.

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Q: Find f, and f, for f(x, y) = 12(6x-3y +8)°. %3D 1,(x.y) = %3D

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Q: Find the least square line y = f(x) = Ax + B for the following data. Xk -2 -1 0 1 2 1 Ук 2 3 3 4 8

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Q: Let f(z) = kz5 + az³ + cz. Find u(x,y) if z = 3.3 + 7.8i, a = 7, c = 11, and k = 3.

A: This is a problem of complex analysis.

Q: Find V (F x G), if F(x, y, z) = 13xi +j+ 7yk and . G(x, y, z) = xi + yj - zk. V. (Fx G) =

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Q: Find the linearization L(x,y) of the function at each point. f(xy) =x° + y° + 1 а. (4,4) b. (2,4)

A: Linearization: - We followed the tangent line to achieve a linearization of a function in…

Q: Find the real numbers x,y,z,t if -3x +y+ zt = 0 3x + y(t – 1) – z(t+ 1) = 0 3x +y+ zt =t+2 - 3x +…

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Q: Consider x1 = et and x2 = v(t)et. If x1 and x2 is linearly independent, then v′(t) = 0. Is this…

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Q: 6. Let z = f(x, y), find and of (a) xy – yz + xz = 0 (b) xz² + 2x²y= 4y²z-3y+2

A: Here z is function of x and y . So to find partial derivatives of z w.r.t. x and y we have to apply…

Q: Let f (x, y) = x² – y² . Find all all points (æ, y) such that Vf (x, y) = ±(1, 1).

A: givenf(x, y) =x2-y2∇f(x, y) =±(1, 1)

Q: Find the linearization​ L(x,y) of the function at each point.  f(x, y) = x2 + y2 + 1  a) (1,2) b)…

A: L(x,y)=f(a,b) +(x-a)fx(a,b)+(y-b)fy(a,b).

Q: Find V. (F x G), if F(x, y, z) = 8xi+j+7yk and G(x, y, 2) = xi + yj – zk. V: (F x G)

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Q: Find V · (F × G), if F(x, y, z) = 2xi+j+14yk and G(x, y, z) = xi+ yj – zk. %3D - V · (F × G) = %3D

A: Given: F→x,y,x=2xi^+j^+14yk^ and G→x,y,x=xi^+yj^-zk^. To evaluate: ∇·F→×G→

Q: Find V· (F x G), if F(x, y, z) = 11xi+j+ 4yk and G(x, y, z) = xi+ yj – zk. V· (F × G)

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Q: Q8) Find the Linearization f(x.y.z) = x² + xy + yz +? at (1,1,2)

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Q: If L(x, y) is the local linear approximation of f(x, g(2, 1)= 4, g,(2, 1)=4 and g,(2, 1)=6, then L O…

A: Use formula of linear approximation

Q: 5) Find ôw/ôv if w=x² +(y/x), x u-2v+1, and y= 2u +v-2, at the point (u, v) = (0,0)

A: We have to find all partial derivatives first.

Q: Find V (F x G), if F(x, y, z) = 11xi +j+ 13yk and G(x, y, z) = xi + yj – zk. V. (F x G) =

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Q: Let F(x, y) = xy + 2y² + 20x + 6y + 33. Find all values of y such that F(y, y) = –2.

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Q: o Find the Vf at the given point 2. (x,y.2)=(x² + y² + ²)² +In.xyz,P(-1,2,–2)

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Q: 2. Show that the function u = p(ry) + /TY p(y/x) provides the equation ‚Pu dy² y² = 0. %3D

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Q: Let F = (3y + 2) i + (4x – 22) 7 + (3x – y) k Find Sc FdF where C is a line segment 8. %3D from A(2,…

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Q: 8. xyzx +2y³ (z, = 1

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Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: Find V· (F x G), if F(x, y, z) = 10xi +j+7yk and G(x, y, z) = xi+ yj – zk. V · (F × G) =

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Q: Find f'(2) where f(t) = u(t) v(t), u(2) = (1,2, –1), u'(2) = (3,0, 4), and v(t) = (t, t2, t).

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Q: Find the linearization of f(x,y) at the indicated point (Xo,Yo). f(x,y) = /x +2y; (4,7) L(x,y) =

A: Given:- f(x, y) =√x+2y To find:- linearization of f(x,y) at the indicated point (xo.Yo). f(x,y)=√√x…

Q: J f ds if Evaluate Of(x, y, z)=x+y, and C is the combinations of lines connecting adjacently the…

A: As per company guidelines we are allowed to solve one question at a time so i am solving first one…

Q: Given the function: f(x, y, z) = æ²y*z³ + xy+ ² + 1. %3D Find a. f,(x, y, z) b. f:(x, y, z)

A: Topic:- partial derivatives

Q: Find the values of ∂z/∂x and ∂z/∂y at the points z3 - xy + yz + y3 - 2 = 0, (1, 1, 1)

A: Given: z3-xy+yz+y3-2=0  At the points (1,1,1) To find: The values  of ∂z∂x and ∂z∂y.

Q: Let F(x, y) = <3x?y3 + y", 3x°y² + y^ + 4xy³,. %3D Evaluate F. dr where C is the line segment from…

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Q: find the linearization L(x, y) of the function ateach point. ƒ(x, y) = 3x - 4y + 5 at a. (0, 0), b.…

A: fx, y=3x-4y+5 Partially differentiating with respect to x, we get fxx, y=31-0+0=3 Partially…

Q: Find f'(3), where f(t) = u(t) · v(t), u(3) = (1, 2, -2), u'(3) = (4, 0, 7), and v(t) = (t, t², t³).

A: Introduction: The outside-inside rule, composite function rule, and function of a function rule are…

Q: Let T : R2 → R2 given by T(x, y) = (2x + y, x − 3y), (x, y) ∈ R2. Determine [T]αα , where α = {(1,…

A: We will find the images of (1,1) and (1,2) under the linear transformation T and then write them as…

Q: Find the linearization L(x,y,z) of the f(x,y,z)= 8 square(x^3+y^3+z^3) at the point (1,2,3)

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Q: Let Ti P(R)→ Pz CR) ope natag T(2+x)=D1 Expilain ke a liness Seech that T (1) = 0. and T(1+x²) = 2x.…

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Q: Fit a quadratic function of the form f(t) = co + cit + czť² to the data points (0, 1), (1, –7),…

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Q: The Wronskian has been computed. Determine whether the functions are linearly independent or…

A: Here given the wronskian of function ex and 2ex is zero.

Q: Let f(x,y,z)=x^3 yz^2+4xy^2 z+y^2 z-2y^4 z^3 find fxyz

A: Use the following formulae, to obtain the solution.…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.