Do the equations x2 + ys + yt? = 13 and y? + x²s + xt2 = 9 define s and t as functions of x and y near the point (x, y, s, t) = (1, 2, 1, -2)? If so, find at that point.

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A: To find- If Wy1, y2, y3 = 0, then y1, y2, y3 must linearly dependent, where y1, y2, y3 are…

Q: Let f(x, y, z) = 5x³ – y + z?. Find the maximum value M for the directional derivative at the point…

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Q: Find fæ, fy, and fz. 4,5 f(x, y, 2) = 4z In (a*y° cos(5z))

A: We can answer all the three question as below.

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Q: Find the relative maximum and minimum values. [6.3] 23. f(х, у) 3 х3 - бху + у2 + бх + Зу - } 24.…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: The function f(x, y, z) = x² − y² − z ² increases in the direction 〈六〉 (1, 1, 1). at the point

A: Please check step 2 for solution.

Q: p) What is the directional derivative of /(x,y,z)=(x+2y+3z)* at point (1,-1,1) in the direction of…

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Q: Find the gradient of the function at the given point. In(x2 - y) - 6, (2, 3) Z = Vz(2, 3) = %3!

A: To find out the gradient of the function at the given point..

Q: 23:- Find and sketch the domain of the following equations:- 1) f(x,y) = Ln(1 – x² – y²) (2)f(x, y)…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Let f(x,y) be a differentiable function satisfying the equation = xy. %3D ду af and After the change…

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Q: 3. Find the derivative of the function f(x, y, z) = xy³ + yz³ + zx³ at the point (-1, 2, 1) in the…

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Q: Find the linear approximation to the equation f(x, y) = 2, at the point (4,2,4), and use it to 2 %3D…

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Q: Find the linearization L(x, y) of the function f(x, y) = V161 – læ2 – 16y² at (-4, –3). L(x, y) = ||…

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Q: The gradient of f(x,y,z)=xy2z3f(x,y,z)=xy2z3 at the point (1, 1, 1) is

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Q: If Wly, , y2. Yal = 0, then (y1, y2 , y3) must linearly dependent, where y1, y2 , y3 are…

A: Given that if  W[y1,y2,y3]=0, then {y1, y2,y3} must linearly dependent, where y1,y2,y3 are…

Q: Find the linearization of the function z = x/j at the point (3, 64). L(x,y)

A: According to the Bartleby guideline only one question can be solved at one time, post the remaining…

Q: Let f(x, y, z) = 5x³ – y + z?. Find the maximum value M for the directional derivative at the point…

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Q: 2. (a) Find the linear approximation L(x, y) near the point (1, 2) of the function f (X,Y)=(0=Y) +…

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Q: If Wly, Y2 Y3]= 0, then (y1, y2, y3) must linearly dependent, where y1, y2 , y3 are diffferentiable…

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Q: 7. Find and classify all stationary points of the function f(r, y) = 1 +y? - 12r + 6y-3

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Q: (6) Find the orthogonal trajectories of the family of curves y = ax? + 4ax + 4a, where a being…

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Q: What does it mean for the differentiability of a function if only one of the Cauchy-Reimann…

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Q: What does it mean for the differentiability of a function if the Cauchy-Reimann equations (Ux = Vy…

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Q: Determine D,f(3,-1,0)for f(xy.z) = 4x-y'e in the direction of i = (-1,4,2, (Express your final…

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Q: Find the directions in which ƒ(x, y) = (x2/2) + (y2/2) (a) increases most rapidly at the point (1,…

A: We have to find the directions a) Given function is  f(x, y)=x22+y22∆f=∂f∂xi^+∂f∂yj^∆f=122x i^+122y…

Q: 17. Determine the equation of the family of orthogonal trajectories of the the family of curves…

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Q: Calculate fw(-1, 2, 0, –1) where f(x, y, z, w) = xy²z – xw² – e2a²-v²-²+2w²

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Q: 5. Determine whether the functions y, and y2 are linearly dependent on the interval (0,1). Yi = 1+…

A: Linearly independent of the function. Using Wronskian

Q: 7) Let Z.= 3x2 - y² . Find all points at which |VZ| = 6 %3D

A: There is an ellipse,  all points on the ellipse are the solutions of given equation.

Q: w = 3x² – 5y² + 2z², (1,1, –2)

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Q: Consider a function of 3 variables h (x, y, z2) = -3 (2+ Calculate the value of its third order…

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Q: 2. Show that cos(wt – B), coswt, sinwt are linearly dependent functions of t. Show Complete Solution

A: Given that: cos(wt-B), coswt, sinwt

Q: Find the linear approximation to f(x, y, z) = at the point (3, -2, -2): f(x, y, z) Z

A: To find the linear approximation of the below function at the point 3,−2,−2. fx,y,z=xyz

Q: 17. Determine the equation of the family of orthogonal trajectories of the the family of curves…

A: Given; y2=2x+c Now differentiate the given function with respect to x.…

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Q: Use the method of variation of parameters to produce a general solution of the inhomogenous equation…

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Q: Determine the linearization of y = 4 – 2x at (1, 2). Then use it to approximate the value of y when…

A: It is given that, y=4-2x2  at 1,2 we have to determine the linearization of function. Then use it to…

Q: 3 Q1// :- find fy,fy at point (4,1) for f(x,y) = Xe

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Q: Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1, 2).

A: Evaluate : ∫∫T(x-y)dA        ......(1) ∫∫Tx-ydydx T is the region enclosed by the triangle. Region…

Q: Find the linearization of the function f (x, y, z) = -6xy+ 9yz + 8zx at the point (1, 1, 1)

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Q: xy" – 2y' +=y = 7x5 Given that y, = x² and y2 = x are 2 Linearly independent soluti homogenous…

A: Introduction: The formula for the particular solution by variation of the parameter is given by,…

Q: z=f(x, y) = 2x +3 y at the point (2, 2, 20) (ii) Use a linear approximation to estima

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Q: Find the linearization of f(x,y) at the indicated point (X0:Yo). f(x,y) = In (x +y); (6, 1) L(x,y) =

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Q: -f(x,y, z) = 2z3 – 3(x² + y²)z + tan-1 xz , (1,1,1)

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Q: Find the orthogonal trajectories of x2 + y? – 2cy = 0

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Q: Find the orthogonal trajectories of the given family of curves x^2 + y^2 = c^2. *

A: Curves:  x²+y²=c²

Q: Find the linearization of f(x,y) at the indicated point (X0.Yo)- f(x,y) = /x + 2y; (1,6) L(x,y) =

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