Ut +Uxx =0 , Uxl0,t) =0, t7. Ux (1,f) = 0, t70 O

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

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Q: the equation of the tangent plane where z=x^2 - 2xy - y^2 -8x + 4y

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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: Find the ar ea of sur face x - 2y - 2z = 0 that lies above the triangle bounded by the lines x = 2,…

A: Given :          The surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x…

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y): 4x sin(xy)…

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Q: Find the directional derivative of f(r,y, z) = e² cos(Tyz) at (0, 1, ) in 2-1 -y-1= I-2 the…

A: To Find: Directional derivative

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 5x sin(xy)…

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Q: Find the equation of the tangent plane to z = In(x?y) – x/ỹ at (-,4). %3D

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Q: wn is bounded by the line y = − 5x + 4, - -axis and the y-axis. y X

A: we will find the area.

Q: F - dr where F(x, y, z) = (4.25yz cos(xyz), 4.25xz cos(xyz), 4.25zy cos(ryz)) Evaluate п 1 and Cis…

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Q: 4. para t> 0, 0 <x < 2 u(0,t) = u(2,t) = 0 u(x,0) = x (2 – x), ди (x,0) = 0

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Q: Show that f(z) = x ² + y ² where z = x + iy is not analytic anywhere using Cauchy Riemann equations.

A: Cauchy Riemann Equations: Given,  f(x+iy)=u(x,y)+iv(x,y)  and it should satisfy  ∂u∂x=∂v∂y and…

Q: The value of the line integral fydx + xydy over the straight-line path C from (0, 0) to (1, 2)…

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Q: A _____ is the set of points (x, y) in a plane such that the difference in distances between (x, y)…

A: The standard form of the equation of the hyperbola is,

Q: Solve using method of variation of parameter: 4y" - y = xex/2, y(0) = 1, y'(0) = 0.

A: Let us consider a second order differential equation with constant coefficient , y''+ay'+by=Q(x) To…

Q: I. Determine la ecuación del plano tangente a la superficie dada en el punto especificado 1. z = 4x2…

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Q: Consider a closed rectangular box with dimensions xx  ft by  yy  ft by zz ft. If xx  is increasing…

A: Proceed as shown

Q: The temperature at a point (x, y, z) is given by T(x,y,z) = 200 e-x- 3y-9z) where T is measured in…

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Q: The diagram shows a small block B, of mass 0.2kg, and a particle P, of mass 0.5kg, which are…

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Q: The projectile is thrown at the angle of 45 degrees with the initial velocity of 1 meter per second.…

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Q: Determine una ecuación del plano tangente a la superficie dada en el punto especificado *:(-4, 2,…

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Q: Find the length of the longest straight line that lies entirely within the surface: This will from…

A: (d) To find: The length of the longest straight line that lies entirely within the surface. Given…

Q: Suppose that we start at the origin in the xy-plane and take n unit steps (i.e., each step is of…

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Q: Suppose that f(æ, y) f(x, y) in the directional (1, – 1) and at the point = xy. The directional…

A: Here, the given function is: f(x,y)=xy So, ∇f=∂f∂x,∂f∂y⇒∇f=y,x⇒∇f(4,-3)=-3,4

Q: ompute the line integral ∫C [2x3y2 dx + x4y dy] where C is the path that travels first from (1, 0)…

A: The line integral is given ∫C2x3y2dx+x4y dy Consider fx,y=x4y22. ddxx4y22=12·4x3y2+22x4y…

Q: Suppose that f(r, y) the point (r, y) 3 (6, ry. The directional.derivative of f(z, y) in the…

A: Given:  fx, y=xy To Find:  To find the direction derivative of fx, y at the point x, y=6, -4, in the…

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: on of the tangent to y = 3e" + 3ex that is parallel to

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Q: azu azu (a) Verify that u satisfies ax2 = = 0 , if u = e* sin y. ay?

A: NOTE:Kindly repost the other question as a separate question.

Q: 5, find dt when r = 3. dt Let A be the area of a circle with radius r. If %3D %3D

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Q: If 2x^4 + x^2y^2 - y^8 = 3x^2 + 4,what is the value of dyldx at point (4,1)? %3D

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Q: 22 Find the Directional Derivabive of Pary,z)= xg-y2'+Z at the point CI, -2, 0) in the direcbion of…

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Q: Find the directional derivative of f(x, y, z) = xy²z³ at P(3, 1, 1) in the direction of Q(0, -5, 7).…

A: Given function: fx,y,z=xy2z3

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

A: Given problem is :

Q: cotu. vX + vy + y %3D If u = show that x ax ay = CoS coS х - у

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Q: If, for V = V (t), tsin(V) = cos(V)+ In(t), then: a) V'(t) = 1 – tsin(V) t(t cos(V) + sin(V)) b)…

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Q: ċ alculate Flux of F= through from 13,0). to.lQ,3)]. ariented live segment upward. 10,3) 13:0)

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Q: Show that the surfaces S1 : 4x + y° + 9z² = 108 and S2 : xyz = 36 are tangent at the point (3, 6,…

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Q: write the line thraugh y S.0;?) (5,0, in the dircetion of 2 vcetor parametruc امپري؟

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Q: Integrate f(x,y, z) = 2x – 3y² – 2z+3 over the line segment from the origin to (1, 1, 1) and over…

A: A parametric curve is a normal curve where we choose to define the curve`s x and y values in terms…

Q: In the standard (x,y) plane, what is the distance between (3, 4) and (6, 2)?

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) 5x sin(xy) at…

A: We have to find the direction in which the maximum rate of change occurs for the function…

Q: integrate ƒ over the given curve. ƒ(x, y) = x2 - y, C: x2 + y2 = 4 in the first quadrant from (0, 2)…

A: The given curve C is a circle with center at origin and radius of 2 units. Let the parametric…

Q: Use a linear approximation to estimate V29. Show the work. Do not round your

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Q: Evaluate the line integral 3xy ds where Cis line Segment Joining (-5,7) to (3,1) the

A: Introduction: A line integral in calculus is an integral where the function being integrated is…

Q: Evaluate | xyzdx + In(xy)dy + xzdz over the straight line segment from (2, 1, 1) to (–1,1, –2)

A: We need to evaluate integral∫Cxyzdx+lnxydy+xzdz over the line segment from 2,1,1 to -1,1,-2.

Q: Find the length of curve along y = x² from (0,0) into (2,4).

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