I – 1 f(r) = I +1 f(x): that are parallel to the line x – – 2y = 2.

Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + BỊ.

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Q: Find the extrema of f(x,y) = xy + 14 subject to  x2 + y2 = 18.

A: To Determine: Find the extrema of f(x,y) = xy + 14 subject to                         x2 + y2 = 18.…

Q: Let f(x, y) = 12x² + 7y² + 3x + 3y+ 6 Find D = frz · fy – fåy-

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Q: find f given f (z, y) = e + 2ry 4y at (0,3)

A: Topic- partial differential

Q: TRUE or FALSE: In the DE with linear coefficients (x – 2y + 4)dx – (3x – 6y + 9)dy, the associated…

A: The given ODE is: x-2y+4dx-(3x-6y+9)dy To check: of the coefficients associated to the DE are…

Q: 2. Show that the function u = e(xy) + VrY 4(y/x) provides the equation Pu = 0. dy? %3D -

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Q: Let f (x, y) = xy2 + 5. Evaluate df/dy at (x, y) = (2, -1) and interpret your result.

A: Given: f (x, y) = xy2 + 5.

Q: Find fryz from the functions f(x, y, z) = 4x³y² – e²y* ++ 4y – x16 %3D - |

A: To find the third order partial derivative of the function fxyz f(x,y,z)=4x3y2-ezy4+z3x2+4y-x16

Q: For the function ex, the linear approximation around x = 2 is %3D

A: Introduction :

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: QO use best linear approximation to (F(Xiy) = ²³ to estimate the value of f at the point (0.0),…

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Q: Q1 If f(x,y, z) = 2 x²y + ez+ Vz Inx %3D Find fr fy and f2

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Q: Given f(x, y) = 3æ'y- 8ry. Compute: www dy?

A: This question can be solved using the concept of partial derivatives.

Q: Find the length of the curve y = Vcos 2t dt from x = 0 to x = T/4.

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Q: 2. Show that the function u p(ry) + Vry v(y/x) provides the equation Pu = 0. ду? dx²

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Q: 6) If F = (3x²y – z)i+ xz3 + y*)j – 2x³z²k, find V(V - F) at the point (2,1,0).

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Q: Find the linear approximation to the equation f(x, y) = 2, at the point (4,2,4), and use it to 2 %3D…

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Q: Find the linear approximation of the function f (x, y) y- 1 at (0,0) x + 1

A: We are given fx, y=y-1x+1. Here, we need to find linear approximation at (0, 0). Now, fx=∂∂…

Q: 2. Show that the function u = p(xy) + VTÝ v(y/x) provides the equation „Pu dx² 0. dy²

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Q: Suppose that f(x, y) : at which {(x, y) | 0 < x < 4, – x < ys va}. 1+ x D

A: Consider a given function:  The objective is to evaluate the following double integral of fx, y…

Q: Find fx , fy and fz. 1 -1 f(x, y, z) = tan %3D \xy²z4, ().

A: Here we will find Fx,Fy,Fz;

Q: Find the quadratic approximation at (0,0) for f(x,y) = e^(x+y) * (xy-1).

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Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + B.

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Q: 4. Suppose that z = x³y, x= t², and y = t³, find . dt = 12t11 dt 11t10 b) = 10t° dt d) = 9t® dt

A: This question is related to differentiation, We will solve it using given information.

Q: find given f (x, y) = eª + 2xy² – 4y at (0, 3) af dy'

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Q: 2. Show that the function u = p(xy) + Vry ý(y/x) provides the equation n, = 0. dy? U -

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Q: Consider the finction f(x,y) = x² + xy – 5x – y+ 1. Then:

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Q: |dx + N(x,y)dy = 0 x² + y,

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Q: Find the quadratic approximation at (0,0) for f(x,y) = e^(xe^y) .

A: Solution:

Q: Find the local linear approximation to f(x, y) = 4x² + y² at P(2,3)

A: We have to find the linear approximation of above function at (2,3) please see the explanation…

Q: Fínd a differentiable curve y(x) that minimizes J = +

A: The objective is to find the differentiable curve yx that minimizes J=∫01y'x2+c2yx2dx if y0=0 and…

Q: Find fr and fy- f (x, y): 6e dt 4 fa(x, y) = fy(x, y) =

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Q: 94: For the system presented by the function x +y+ 2 4xy. Calculate all the possible points at which…

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Q: Q) Compute for y(x) sec (2x) + 2x -1 and x(t) = 4cos(t) at t-1

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Q: Integrate h (x. y.2) = yzi+xj+xzk over the indicated path: the line segment from (0. 0. 0) to (1. 1,…

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Q: y = secx prove that d² y dx +y 2y

A: For y=sec x, we need to prove that d2ydx2+y=2y3. Here,            y''=secx''      =secxtanx'…

Q: If y = x(x – 1)* then y' at z = 2 is equal to

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Q: Find the interval on which the curve 1 dt 4+t+ 2t2 is concave upward.

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Q: Q3) for f(v) = sec2 (3v-1) and g(v) = tan2(3v- 1) show that %3D S(v) = g'(v).

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Q: 2. Show that the function u = p(xy) + Vxy v(y/x) provides the equation = 0. dy? -

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Q: Suppose that f(x, y) = e 42? - ly + 7z + 2y then find the discriminant of f.

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Q: Find the linear approximation of y = V1+ x at x = 0 and use it to approximate V1.05 7.

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Q: 8) Confirm that the stated formula is the linear approximation at x =0 %3D (1+x) =1+15x

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Q: 2. Let f(x,y) 3x y. If C is the line segment from (1,1) to (2,3), evaluate r'dt.

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Q: Integrate h (x, y. 2) = yzi+xj+xzk over the indicated path: (a) the line segment from (0, 0. 0) to…

A: definite integrate calculus

Q: Find f (1, 1) S(x, y) = In( %3D Vx² + y²

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Q: Q5.a) Find if sec?y = x² + S t² dt Jsiny

A: P.S.: please ask one question at a time.

Q: 1 V1 – x z 1 – at x = 0 x, 2

A: Since you are asking part (c). We are answering only the (c) part for you.…

Q: Find a function f:R² → R, its tangent plane at the point (1; 1; f(1; 1)) is given by -2x – 9y – z+8…

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