f(x,y) = 3x-x- 2y ty faa(ay)= -6x fyy (3,9)= 123°-4 D(x.y) = faafyy-[tay]²- - 72ny² +24% ニ 12ay2+ こ Saddle or max,Min, Not a Critial pont (,-1)= %3D (1,) =

Q: 2x + 7x +3. If Ax = 0.3 at x = 4, use linear Let y approximation to estimate Ay %3D %3D %3D Ay =

A: Given y=2x2+7x+3 if ∆x=0.3 at x=4 we have to approximate ∆y using linear approximation.

Q: 5. y" + y = 2t, y(1) = 1, y'(1) = -2, yp(t) = t² – 2t 6. y" + y = 2e-', y(0) = 2, y'(0) = 2, yp(t) =…

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Q: (c(2z+y), %3D ue of c in the joi F of W.

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Q: Let y = 2x + 2x +3. If Ar = 0.2 at a = 2, use linear approximation to estimate Ay %3D Ay Submit…

A:

Q: 2. When object P, with mass m, , moves at v, and object Q, with mass m,, moves at v,, the velocity…

A: Given,For P, mass = m1  and velocity = v1Let, velocity after collision is u1For Q,mass = m2 and…

Q: 2. Find the equation of the tangent plane and the normal line at the point (0 ,1 , 2) on the surface…

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Q: If f(z, v) – 4z°y+ 8zy, then the total differential of f at z-1 and y - 1is: O df - 17 dz + 22 dy O…

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Q: (b) u = Vt² + 2vt3 - 1 tan I (d) y = sec I VE-1 (f) y = VI+1

A: Since you have asked multiple subpart, as per our guidelines we are supposed to answer only first 3…

Q: 8. Find the flux of F = (2x – 5y², 3y, x) out of the sphcre of radius 2 centered at the origin.

A: The flux of the vector space is given by the formula, ∫S∇.F dS where S is the sphere of radius 2…

Q: d²y dy dt + 81y = 0, y(0) = 9, y' (0) = 3 + 18- %3D %3D dt?

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Q: dy If y = (t + 2t + 8) (6t² + 6), find %3D dt dy dt

A: The given question can be solved as shown in step2.

Q: s) find the general sduton of second dilferential equation 3y"+2y'+y=0

A: Consider the given differential equation 3y" + 2y' + y = 0

Q: Find the location and velocity at t = 4 of a particle whose path satisfies dt dr (3t-1/2, 5, 8t) and…

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Q: Resuelve la ecuación integro-diferencial y'(t) = cos t + y(7) cos(t - 7) dT, y(0) = 1 %3D

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Q: (a) A beam is fixed at its left end x = 0 but is simply sup- ported at the other end x = L. Show…

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Q: Evaluate (2х — у) dx + (х + 3у) dy. C: elliptic path x = 4sin(t), y = 3cos(t), from (0, 3) to (4, 0)

A: Line integral

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

A:

Q: მს For the function (x, y) = √√x²y², we have that 8 (0,0) = 0 and (0,0) = 0. From this, it follows…

A: As per the question we are given an argument about the first order linear approximation of the…

Q: Determine the local linear approx imation of flx,4,z) =(1+x) (l-y³) (l-2)²' at the point CT, 2,3)

A: The local linear approximation: Lx, y, z of the function f(x, y, z) at the point x0, y0, z0 is…

Q: Show that the displacement u(x, t) in an elastic string of length t fireed at both ends which is set…

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Q: Suppose w = x³yz + xy +z+3 and x = 3 cost, y = 3 sint, z = 2t. Then dw dt t= . [Show solution.] =

A: Given :w=x3yz+xy+z+3x=3costy=3sintz=2t

Q: Let æ – 3y3 – z° + 2xyz – 398 = 0. dz dz and at the point (– 1, – 5, – 4). Use partial derivatives…

A: i am solving 1st question for 2nd question repost.

Q: Line WY bisects Line UV at Y. If UY = 2x + 1 and YV = x +7, find UV.

A: Meaning of biscsts is dividing into 2 parts .

Q: Integrate f(x,y) = x-5y over the curve C: x +y = 64 in the first quadrant from (0,8) to (V32,/32).…

A: Formula Used:Line integral ∫Cf(x, y) ds=∫abf(x(t), y(t)) dxdt2+dydt2dt

Q: Find the symmetric equations for the normal line LN to the surface S:f (x,y) = 5VT +y? at the point…

A: Given function is S:fx,y=5x2+y2. We have to find the symmetric equation for the normal line LN to…

Q: Find the Second appoximation for the System. X Sin y at (xo,,)= (1, 1). y=Cosx

A:

Q: Find the moment of inertia with respect to x-axis the aarea bounded by 2y^2-8y-16x=0 and the line…

A: The moment of inertia is the rotational analogue of mass. The expression for moment of inertia is…

Q: 2. Prove that the directional derivative of f(x, y, 2) = ry sin z at (1,2, ) in the direction v = i+…

A: Given:        fx,y,z=xy sinz         x,y,z=1,2,π2    direction v=i+2j+2k   Differentiate the…

Q: ihe fcu,v, w) and its partial derivatives with respect tou and vand w and are Continous that u-メ-ツ…

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Q: The two functions x(t) and y(t) satisfy the simultaneous equations dx/dt - 2y = -sin(t), dy/dt + 2x…

A: Given: dx/dt - 2y = -sin(t), dy/dt + 2x = 5cos(t)

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: dy at z = 5 if y = 5x² + 4 and dt dz Find 3. dt dy dt

A: Given y=5x2+4 -1and dxdt=3

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: Assume that a body moving with velocity v encounters resistance of the form dv/dt = -kv3/2. Show…

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Q: Let y 4x + 3x + 4. If Ax 0.3 at a = 3, use linear approximation to estimate A %3D Ay =

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Q: If f(z,y) = 3z² - 8y, then the total differential of f at z =1 and y = -2 is: %3D O df = 6 dz + 32…

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Q: dy If y = (t + 5t + 6) (2t² + 4), find dt dy %3D dt Submit Question

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Q: Find the Saution of the equation using Inver's operator method y + 3y + 2Y = 4 cos(x)

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Q: Let y = 4x + 2x + 4. If Ax = 0.1 at x = 2, use linear approximation to estimate Ay %3D %3D Ay 2

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Q: dz dt 3x – 2y fip dt 9x - 3y %3D z(0) = 1 %3D

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Q: Let y = 3x +7x+ 4. If Ax = 0.4 at a = 1, use linear approximation to estimate Ay %3D Ay 2

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Q: Find all the second partial derivatives (including fxy etc.) a) v = sin(2s^2 − t^3)

A: Please see the explanation below

Q: What is the integrating factor of (ry + y) dr + (r + 2y-1) dy %3D

A: Given xy+y2dx+(x+2y-1)dy=0Compare above differential equation with…

Q: 10. Find the work done by the force F=vx +2y y - 7 for a particle that moves between points (-1,0,1)…

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Q: (b) Find the partial derivative at point (u,v) = (-4,0) of w = In(xª + yß + zª),x = ue"sinu, y =…

A: Chain rule:  Suppose that  are differentiable functions of and  is a differentiable function of .…

Q: ds Find where Vt +s = 2s . %3D dt

A:

Q: Find fr and fy- f(x, y) = fetlo dt f.(r, y) = fy(x, y)

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Q: dz dt || z = cos(x + 3y), x = 8t³, y = 9/t

A: By the use of chain rule we need to find the required derivative.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.