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Q: 29, + 16y=0 geoJ = 2, go)= -2 2. 31, dy dy -54 =0 dt

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Q: dx =- 1. dt dy at x = 2 if y = 4x° – 2 and dt %3D Find - dy dt

A: Given: y=4x2-2 and dxdt=-1 To find: dydt, when x=2.

Q: Find a function w = ƒ(x, y) whose first partial derivatives are ∂w/∂x = 1 + ex cos y and ∂w/∂y = 2y…

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Q: Find the requested partial derivative. dz 3 if z° = z+ xy - 1 and y = x+ y- 1 dy 3

A: We have to find partial derivative

Q: Obtain the particular solution satisfying the initial condition indicated. (variable separable) dx…

A: Use the variable separable method and satisfy the initial condition. Also use the properties of…

Q: If f(x, y) = y² cos(x) – a° In(y), find the second partial derivative

A: Partial derivative problem

Q: 3. Find the second order partial derivatives and of ôx' ôy'êxôy Ôyêx S(x, y) = x² - cos.x+6y' +siny…

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

Q: 4) S(x, y) = (4x-x* )cos(y) on the Ans. Absolute max.: 4 at(2,0) 3/2 Absolute min.: at 2 rectangular…

A: Given

Q: Find the value of ∂z/∂x at the point (1, 1, 1) if the equation xy + z3x - 2yz = 0 defines z as a…

A: Given, the equation xy + z3x – 2yz = 0, defines z as a function of two independent variables x and y…

Q: Evaluate (2x-y)dx+(x+3y)dy along the path C: curve on y = 1-x² from (0,1) to (1,0).

A: Given the line integralI=∫C(2x−y)dx+(x+3y)dyCurve y=1−x2

Q: Suppose z = f(x,y) is a differentiable function of two variables. What do the partial derivatives,…

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Q: If f(x, y) = 3x² – 7y, then the total differential of ƒ at x = 1 and y = -2 is :

A: we need to find the total differential of the function  f(x,y) = 3x2 - 7y2 the total differential,…

Q: If f(x, y, z) = 12ry - 2yz - 6zx + 7, then the first order partial derivative f = O - (2y – 6x) (2y…

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Q: Solve for the partial derivative with respect to x, y and z f(x, y, z) = x²y + xy² + 2xyz

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Q: 36. Using the approximation dy dy h dr * Yn+1- y. and that dr 1, y = 2 when r 0. Then, y A h- 2 h+ 2…

A: Please see the answer below.

Q: Find the first partial derivatives of 3x - y f(x, y) = 3x + Y at the point (x, y) = (4, 4). af (4,…

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Q: A particle moves on the circle x2+y2=25 in the xy-plane for time t≥0. At the time when the particle…

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Q: In Exercises 28-34, find ƒx , ƒy , and ƒz .

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Q: 2(a) Given that f(x,y) = 6x'y³ - cosx + 5y- siny + 10x, establish %3D the fact that, the order in…

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Q: Find the first partial derivatives with respect to x, y, and z. Ex, y, 2) = 3x?y - 6xyz + Byz? ,(X,…

A: We have to solve this problem by partial derivative method.

Q: Suppose that the partial derivatives of a function ƒ(x, y, z) at points on the helix x = cos t, y =…

A:

Q: Find the partial derivative of f(x,y) with respect to y at the point (3,2) f(x,y) = ln(x^2y-xy^2)

A: A partial derivative of a function of several variables is its derivative with respect to one of…

Q: Find the differential dz of the function f(x, y) = 4y² + x²y-2xy and use it to approximate Az at…

A:

Q: 11. Find the length of the curve x = on the interval (2, 4] (integrate with respect to y) 12y3 un

A: Given that the function x =y55+112y3 Find the arc length of the graph of the given curve on the…

Q: Estimate Ay using differentials. .1/3 y = x¹/3 e³x-1, a = 1, dx = 0.1 -

A:

Q: 11. Show that the function 2ry when r + y + 0 h(r, y) = 0; when r = y = 0 has partial derivatives…

A: Given: h(x,y) =2xyx2+y2;     when x2+y2≠00 ;      when x=y=0 To show that the partial derivative…

Q: 8. Find a continuous solution satisfying dy dr + 2xy = f(x) where = x if 0 < x < 1 0 if x ≥ 1 off…

A: Solve the following

Q: Evaluate the deflection of a vibrating string of unit length having fixed ends with initial velocity…

A: Consider the wave equation    ∂^2u∂x2=1c2∂^2u∂t2     .....(1)   here U(x ,t) is the defection of the…

Q: What is the result of the partial derivative 3(z² + y sin (z)) Select one: a. 2a + y * cos(x)

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Q: Show that the Second Derivative Test is inconclusive when applied to the following function at…

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Q: 46. s(х, у) tan (y/x) -1 =

A:

Q: Compute Y (II) withe y" y'= -8 (Sinx+cosx. Y(T) = 0, y¹ (F) --8, by @ Taylor Series

A: Given differential equation is y''-y'=-8(sinx+cosx)     (1) and y(π)=0, y'(π)=-8 Solution a: Using…

Q: SM 6. Suppose that f (x, y) has continuous partial derivatives. Suppose too that the maximum direc-…

A: Theorem: Let fx, y be a function with continuous partial derivatives. The maximum value of the…

Q: The time rate of change of liquid circulating in two tanks is govemed by dy -0.02x + 0.02y, = 0.02x…

A:

Q: 2) Let f(x, y) = x sin(2y) + 5y¹. Find fyyyyyyyyyy (x, y) (10 partial derivatives), explaining how…

A: Here the given function is f(x,y)=xsin(2y)+5y4x. We have to find the 10 times partial derivative of…

Q: 1 The partial derivative of f(x, y, z) = Arctan with respect to z is xy? z³

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Q: What can you conclude about a real function f(x,y) that has continuous partial derivatives at a…

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Q: (1+x^3) dy-x^2ydx=0 satisfying the initial condition x=1, y=2

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Q: d²x dx 5 dt2 2- 3x = -9t2 – 1 - - dt dx When t = 0, x = 1, = 0, find x when t = 2 dy %3D -

A: Please see the below picture for detailed solution.

Q: cos v f(x, у, 2) 3D xz2 af af 2 cos y Cosv siny df = - = - = - dx x2z2' dy dz xz3 XZ af cos v %3D af…

A: Topic:- partial derivatives

Q: Find the value of dx at the point (1,1,1) if the equation 6xy + z"x-2yz = 5 defines z as a function…

A: Given: (x,y,z)=(1,1,1) and z=6xy+z4x-2yz-5=0

Q: Find all the second partial derivative T = e-4r cos(0) -4r, Trr 16e 'cos (0) %3D Tre = 4e -4r,…

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

Q: dt What is the linearization of h(x)= 6+ at x=1? cos (1 -1)

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Q: 1 transforms the equation x dy + y = xy2sin(x) into The change of dependent variable y = dx dv A.…

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Q: 1-fd dydx R = {0,1} * {2,5} y2 2-S y2 (1–5x)2 dxdy R = {0,1} * {0,2}

A:

Q: (b) Form the partial equation by eliminating function f from z = f(x?

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Q: ди + 3x- = 1 + u, dx ди -co 0, dt u(x, 0) = f(x).

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Q: d²x + cos(t)- dx sin(t)- + sin(t)x = tan(t) dt dt2 x(1.25) = 6 dx = 5 dt 1.25 has a unique solution…

A: The differential equation  d2ydt2+ptdydt+qty =rt                    .......1 with conditions yt0=y0,…

Q: Find all the first partial derivatives of; glw,2, y, z) = xe2w - wyz?

A: Topic:- partial derivatives

Q: Solve for the partial derivative with respect to x, y and z f(x,y,z) = x²y + xy² + 2xyz

A:

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.