6. Let f(x,y) = sin(x + y) + arcsin (xy) a. Find the linearization L(x,y) at the point (0, ")

Q: Let f(x, y, z) = In(x² + 2) + y²e== – cos(2yz). Find fzyz- %3D

A: Given that: f(x, y, z)=ln(x2+z)+y2exz-cos(2yz)

Q: Apply runge kutta method of order two on du/dx = sin(xu), u•=0.1,h=0.1 to find u(0,3)

A:

Q: 4. Let f(x, y) = 2TY x = In 2 g and y = In s. . a. Find the equation of the tangent plane to f(x, y)…

A: Let f(x,y)= 2xy , x=t/ln2 and y= lns Here we have to find the equation of the tangent plane to…

Q: Find dy for all of : dx 1- y = x/Inx у

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Q: (b)Find the derivative of g in the direction of a= 2i+ curl w where at point (0,-1,1) g = In- 4 + 2…

A: Given, w=cosxyzi+xeyz+1j+xyzk Then, Curl…

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: Let y = tan(2z + 3). Find the differential dy when z = 2 and dr 0.1 %3D Find the differential dy…

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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: Let y = tan(2z + 3). Find the differential dy when z = 2 and dæ = 0.4 Find the differential dy when…

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Q: Show that if the function f(x, y) = ex siny + ecosx, satisfies Laplace Equation.

A: We can solve this as follows:

Q: In(xy) cos(Tx + T) when x 2 and y = 1/2.- Find the tangent plane to f(x, y)

A: We have to find the equation of  tangent plane.

Q: 21 (important) Find the fixed point for F(x) = ax + s. When is it attracting?

A: Given Fx=ax+s

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Q: Find Fxx and Fxyz of: XX хуz y2+Cos (xz) f (x, y, z) : 2 Siny

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Q: - Sva cos 2t dt from x= 0 to x= Find the length of the curve y =

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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: Let w = x2e2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y =…

A: Given: w=x2e2ycos3z x=cost y=lnt+2 Putting x, y and z in w, we get…

Q: (b) Find the derivative of g in the direction of a=2i+curl w at point (0,-1,1) where u u +2 g= In. J…

A:

Q: Let w = x^2e^2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y…

A: Given  By chain rule of differentiation , we have

Q: HW 0 1f y=tanx show thats y" = -2Siny Cosy %3D

A:

Q: Find the linearization L(x,y) of the function f(x,y) = e 3× cos (9y) at the points (0,0) and 0,

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Q: -IVEN DIFFERENTIAL EQUA quation 1) dx + (x -u) du = 0

A:

Q: 1. Give an equation of the tangent plane to the surface z = In(4y – x) at the point (3,1,0). 2. Use…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let y = tan(4x + 8). Find the differential dy when x = 4 and dx = 0.3 %3D Find the differential dy…

A: ? 1.2sec224 ?2.4sec224

Q: The equation of the upper semicircle centered at the origin with radius R in parametric form is…

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Q: Find a homogeneous (linear) DE with a following FSS: y1(x) := 1; y2(x) := sin(5x); y3(x) := cos(5x)

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Q: 1. If y=tanx, prove that y=2(y² +1)(3y² +1).

A:

Q: Let y= tanx .(a) Find the differential dy .(b) Evaluate  dy and ∆y if x= and π /4 and dx =-0.1.

A: Given function is (a) Differentiating with respect to x, we get

Q: 4. Curl of f (x, Y, z) = 2xyi + (x² + z²)j + 2zyk is

A:

Q: aーメ ターメ2.y to い-X to cylindHcal coordin ates

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Q: If Z = Jxy +y, x= cos 0 , y= sin 0 when 0 dz By using chain rule find de

A: Chain rule for one independent variable- Suppose that x = g(t) and y = h(t) are differentiable…

Q: Let f(x, y, z) = ln(x2 + z) + y2exz − cos(2yz). Find fzyx.

A:

Q: Use the Chain Rule to find az/ðs and ôz/dt. z = arcsin(x – y), x = s² + t?, y = 2 - 2st as az at II

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Q: В. Find dz/əx , əz/əy at the point (1,1,1) if x³ + z² + ye*z + xz cos y = 0 .

A:

Q: Let y = tan(3r + 4). Find the differential dy when z = 2 and dr 0.1 %3D Find the differential dy…

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Q: Let y = tan(4x + 4). Find the differential dy when x = 5 and dx 0.4 %3D Find the differential dy…

A: Given : The function y = tan(4x + 4)   To find : Differential dy when, 1. x = 5, dx = 0.4 2. x =…

Q: The direchional derivative of the salan funchion at (l,-1,0) in the direction (i-j+2k) is xy- z- xyz…

A: Given that  Let f(x,y,z)=x^2y-y^2z-xyz To find the directional derivative at point

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A: According to chain rule of differentiation .According to product rule of differentiation . According…

Q: #2. Show that the line integral (sin y dx + (x cos y – sin y) dy)

A:

Q: Siny dx t sin Zydy + x dy

A: To solve: sin⁡ydx+sin2⁡ydy+xdy=0…

Q: Compute ∫C(ln(x + 5) - x2y)dx + (xy2 + sin(ey))dy. C is a unit circle with counterclockwise…

A: We need to compute ∫C(ln(x + 5) - x2y)dx + (xy2 + sin(ey))dywhere c is a unit circle Equation of…

Q: Let C denote the curve of intersection between x = -5z° and y = 6z", starting from A(0,0,0) and…

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Q: 1. If y= tanx, prove that y"=2(y² +1)(3y² +1).

A:

Q: Find dz/ðx , dz/ðy at the point (1,1,1) if x³ + z² + ye + xz cos y = 0

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Q: Evaluate f. 2xcos[y] dx- x² sin[y] dy along the parabola y = (x - 1)2 from (1,0) to (0,1)

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Q: Let f(x,y, z) = In(x²2+ z) + y²e*z – cos(2yz). Find fzyx·

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Q: Determine the linearization of f(x, y) = arctan(x² + y²) at

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Q: implicitly dx

A: Solved below

Q: 2. Suppose that a function f: R3 → R³ defined by: f (х, у, 2) 3 (2х + Зу — z, sin(тхy?z-1),…

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Q: Evaluate [xy dx+(x+y)dy along the curve y=x² from (−1,1) to (2,4). [Verify using Mathematica]

A: