QUESTION 1 af (3,2). Let f(x,y)=x²y*.Find QUESTION 2 af (3,2). ду Let f(x,y)=x²y*. Find

Q: If f(x, y, z) = excosy + z, show that fxx + fyy + fzz = 0

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Q: In Exercises 61-67,firstfind f' and then find f.

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Q: Let f(x, y) = In(2x + 3xy) then 1 fr(1,1) : 2 fy(1,1) = = 5 3x fy(x, y) = 2x + 3xy

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Q: Utt = Uxx, x>0, t > 0, u(x,0) = f(x), u₁(x,0) = 0, u₂(0,t) = 0, where f(x) = { b) Sketch the…

A: solutions are given below:

Q: 4. Find the orthogonal trajectories of the family of curves y= Ce“ + 10

A: Here we have to find the orthogonal trajectories

Q: Suppose X and Y are the coordinates of a randomly sampled point in the triangle with vertices (- O),…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Find f(-1,1,0) f(x,y,z)=(2xy-y^2+z)/(x^2+3xy+z)

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Q: [1] Determine the orthogonal trajectories of y(1+2x?)=ax.

A: The given equation is:y1+2x2=axy=ax1+2x2              ..............(1)

Q: 21. Find div(F), where F(x, y, z) = xyzªi+x²zªj +4x²yz³k. a) -4xyz³+xz4 b) x²y+xz4 c) yz + 3x²yz² d)…

A: Topic = Algebra Correct option = d

Q: Determine (x, y) and 2(x, y), where f(x, y) = X sen(xy) %3D y

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Q: Specifically a differential equations problem. Question in pic below. The first "Select" is either…

A: Here, f1(x)=ex+3 and f2(x)=ex-4

Q: Find the linearization of z = f(x,y) at P(-3, 2) when f(-3, 2) = 2 and f-(-3, 2) = 1, fy(-3, 2) =…

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Q: Step 6 Since F is conservative, we know that f,(x, y, z) = 12yz2 Therefore, h'(z) = 0

A: We have to write value of fz and h'(z):

Q: 4. Let f(x, y)=2x*y' . Find f,(x,y)

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Q: Let g(x) = f() dt, v %3D

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Q: The gradient vector of the function f(x, y) = cos(4x - 6y) is (4 sin(4x - 6y), -6 sin(4x - 6y)).…

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Q: Assume that z = ln (ƒ(w)), w = g(x, y), x = sqrt(r - s), and y = r^2s. If gx(2, -9) = -1, gy(2, -9)…

A: Given Now, we will find partial derivative of w with respect to r and s by using chain rule

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

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Q: f(-1,3) = 4, fr (-1,3) = 5 and fy (-1,3), then the linear approximation to f(-1,3; 3,2) is

A: Formula: The linear approximation of function z=f(x, y) at point a, b is given by, z-fa,…

Q: Let f(x, y) = ln(x + y − 1). Then, ƒ(1, 1) =

A: The given function is;  f(x,y)=ln(x+y-1).

Q: F(1), p(y) - y - 1, F(Y) - F(y - 1), y - 2, 3, ...

A: Suppose that Y is random variable that takes on only integer value 1,2,.. and has distribution…

Q: Evaluate 3xz dV where E {(x, y, z) | 2 < x < 5, x < y < 2æ, 0 < z < x + 2y}

A: Given,

Q: 17. Let f(x, y) = x'y4. Use Eq. (4) to estimate the change Af = f(2.03,0.9) – f(2, 1)

A: You have to just put the value in the function and proceed....go through the solution

Q: 2.2 11, IfF = xyz\+x*y°z}+ xyz k then find div F at (2, 1, – 3).

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Q: (a) The function z depends on u and v so that z = (2u – 1)(1 –v)? , u = x + 2y and v = x – 2y az…

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Q: 3. If f(x, y,z)= In *yz +e tar's="), find f,,fy and f. . хуz

A: we have to find the partial derivative

Q: Let f(x, y, z)= = fz(x, y, z)= fy(x, y, z)= fz(x, y, z)= 2² - 2y² I y² + 4z² Then

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Q: Suppose X and Y are the coordinates of a randomly sampled point in the triangle with vertices…

A: From the given information, Vertices of a triangle are as follows: A =(-1,0) B= (1,0) C= (0,1)

Q: A researcher collected data on ( X , Y ), and wanted to test if the true relationship is linear.…

A: To test whether true relationship is linear or not, consider Lack of fit F-test. H0: There is no…

Q: Find fy (X,y) if f(x,y) = (x° + y°)°. ху Exy(x.y) =

A: Topic: differentiation

Q: Suppose f(x, y) = (2æ)" + 3y". Find f# (1, 1), fy(1, 1), and fyy (x, y)

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Q: A consumer has utility function xy u(x, y) = x+y

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Q: Let f(x, y) = (- (3x + y))'. Then %3D drðy af

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Q: If e**У- ху, then dx x(1- y) A Ax- 1) Ax - 1) B x(y- 1) (1- x) x(y- 1) x(y- 1) (D Ax - 1)

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Q: Find the linearization of f(x,y) at the indicated point (X0,Yo): f(x,y) = In (x² + y); (1, 1) L(x,y)…

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Q: Let v = (3,4, 12) . Find the directional derivative of f(x,y, z) = x – y² +3z³ in the direction of…

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Q: Evaluate F. dr where F(x, y, z) = (3.75yz cos(xyz), 3.75xz cos(ryz), 3.75xy cos(xyz)) and C is 1 1…

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Q: f (x, y, z) = x² + y² + z² and u = (1,0, 1) at P(1, 1, 1).

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Q: Let X and Example 20. PDF 0<I<3, 0<yS3 fxy(r, y) = otherwise Find

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: If w = f(x,y, z) = yzln (xy) + tan-1 then af at point 1,1,1 is : 3 Option 3 Option 1 Ontion 2 1/2

A: Here we are required to calculate the partial derivative of the function f(x, y, z) with respect to…

Q: a) Use the definitlon of derlvative to find ds If dt 2t+1

A: As per bartleby guideline for more than one question asked only first is to be answered please…

Q: Find the linearization of f(x,y) at the indicated point (Xo.Yo). f(x,y) = In (x +y): (4, 5) L(x,y) =

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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: 3. Find general Golution y" + y= Secx

A: Given that, find the general solution y''+y=sec3x (D2 +1)y=sec3x

Q: If ø = 3r²y – y³,2. Find gradient Vø at the point (1, –2, –1).

A: The solution is given as

Q: 2xy F(x, Y) =Vx+ 2y (1, 1) f,(x, y) = 1,(1, 1) S(1, 1)

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Q: If f(x, y, z) = In(x° + yº + 2®) + v(x° + y8 + z®), then find f, fy and f; at (1,1, 1). %3D

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Q: f (x-y/x)=(y/z) then z=[x(z-y)]/y

A: Given that, x-yx=yzz=xyx-y         ...(1)

Q: Let f(x, y) = -4x + 3y. Find the directional derivative in the direction of v = from the point P =…

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

A: Given,          fx,y,z=xyz