A general solution of the PDE uux +yuy is of form y (a) f(u² - x², Y x+u (b) u ² = 8( x + u) y g = X = 0; where f: R² → R is C¹ and Vf ‡ (0,0) at anypoints + x² ; g = C(R) (c) f(u² + x²) = 0, f = C(R) (d) f(x + y) = 0, f = C(R)

Q: f f(1, y) = (3r" + 2y² – 19)*, then fy is given by : 16 y (3z² + 2y² – 19)* O 24 y (3z° + 2y + 19)°…

A: Here, we have to differentiate the given function wrt y only treating x as constant..

Q: Find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously. f(x, y) = x² +…

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Q: T(x,y, z) = x² + 2y² + z

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Q: In(x – y) 9 – x² – y² · /x² + y? – 4 d and sketch the domain of f(x, y)

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Q: (7) (a) Find the linear approximation L(x, y) to the function f(x, y) = √² + y² + 4 at the point…

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Q: For a, b, c, and d: Let h(x) = (f og)(x) a) Let h(x) = (2x-5) and f(x)= x, find g(x). b) Let h(x) =…

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Q: at r s) The linear () is = where A is approximation to f(x) = √√/1 + 8x y = A + Bx and where Bis

A: The given function fx=1+8x. We have to find the linear approximation of fx at x=0.

Q: given f (z) = 32² – 6z + j3, what is the value of u(3, 2)

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Q: Find the general solution of x (z? – y?) +y (x² – z?) = z (y² – x) Z. a y

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Q: Consider 1 y"(t) + 2y(t) + 2y(t) = 1², y(0) = y(0) = 0 2 (a) The complementary function ye

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Q: xux − yuy + y²u = y²

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Q: 6. Find the general solution of X Ury -Y Uyy = Uy %3D by using the change of variables: v = x, w =…

A: Given: The partial differential equation, xuxy-yuyy=uy   To find: The general solution of the given…

Q: Q4: If f (x,y,z) = x?y³ – y²z³ then fy = %3D -

A: Given,           fx,y,z=x2y3-y2z3

Q: f(x,y) = x² + 3y² + +xy b. f(x,y) = /x² + y² a. %3D

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Q: Given the function f(x) = x(x – 3)(x + 2), find 1) its y-intercept: 2) its x-intercepts: 3) As x →…

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Q: Compute the discriminant D(x, y) of the function. ƒ(x, y) = x³ + y4 − 6x − 2y² + 2

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Q: Find the functions x*(r) and y*(r) such that x = x*(r) and y = y*(r) solve the problem max f(x, y,…

A: max fx , y, r=max-x2-xy-2y2+2rx+2ry To Find: x*r , y*r such that x=x*r ,y= y*r.

Q: u(x, y) and let f and g be twice differentiable functions. The al solution to the equation uy2r + 2y…

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Q: In a certain culture of bacteria, the rate of increase is proportional to the number present. (a) If…

A: Model the given problem dpdt=kp if p is the present number of bacteria integrate it on both sides…

Q: Let U(z, y) (2x +3)(y+5). %3D Select the correct expressions for Uz and Uy: (A). Uz= 2x+3. %3D (B).…

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Q: Given f (x, y) = x2 – 6xy + 2y2, determine f (0, 0) f(-1, 2) f (5, 10)

A: Substitute the values for x and y in the function, f(x,y) to determine its value at (x,y) . Consider…

Q: Find the values of a, b and c such that the function s(t) = t + at² + bt + c satisfies s" (t) = 6t +…

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Q: The equations xcos(u) + 9uy2 + e² + 2 = 0 and 3ye" + 4x²v – 3æcos(2) +1 = 0 are solved for u and v…

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Q: Suppose that f(z, y) = e-2-2y –2z+y Then the maximum is

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Q: Consider f(x, y) = (2x² + xy + 1, xy, x² + y²) and let c = (1,-1). Find Df(c) by definition.

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Q: If f(1, y, 2) = In(z³ + y8 + z³) + V(z³ + y³ + z³), then find fr, fy and fa at (1, 1, 1).

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Q: Write the Linear Approximation to f(x, y) = x(1 + y)−¹ at (a, b) = (8, 1) in the form f(a+h,b+k)≈…

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Q: of (V × F) (1,1, 1)

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Q: Suppose f(x, y) = xy² + 3. Determine each of the following: f(0, -2)= f(-2,0)= f(0,0)= f(-3,-2)=…

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Q: Compute the discriminant D(x, y) of ƒ(x, y) = x2y2.

A: fx, y=x2y2 Partially differentiating with respect to x, we get ∂f∂x=2xy2 Partially differentiating…

Q: Find f, and f, for f(x,y)=y In (2x+7y).

A: F(x,y) = y ln(2x + 7y) To find : fx and fy

Q: (b) The function f depends on u, v and t so that f(u,v,t)=u²+v+2t It is further given that (i)…

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Q: 3. Find the (x, y) co-ordinates of the two stationary points of the function f(x, y) 3x² + 6xy + 2y³…

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Q: Let A(t) = 3ti+2]-4k, y B-21-21-3tk and C(t)=-1+3tj+6k. find Ax (B-C) dt

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Q: 2. Let f(x, y) = 4x³y² + 3x²y³, find: (a) Vj (1,2) (b) f(1,2), where u = 17-17

A: (2)  Given that  f x, y = 4x3y2 + 3x2y3  (a)     ∂f∂x = 4y2∂∂xx3 + 3y3∂∂xx2       ⇒ ∂f∂x = 4y23x2 +…

Q: (a) Let r(t) = ti+tej+fk. Find ((1),4 × (?),1) - (1)a tuj

A: First we find out first derivative of r(t) with respect to 't' then find out 2nd derivative and then…

Q: Problem : If f(x, y, z) = In(x³ + yl2 + 2) + V(T12 + y+ 2), then find fz, fy and f; at (1, 1, 1).…

A: We have to find partial derivative

Q: T: M22 --->M22 defined by T(A) = AB,

A: Given, a matrix B, and defined a map T(A) = AB, where T: M2×2  ---> M2×2. We have to find the…

Q: Show the function T : R² → R³ given by T(x, y) = (x − y, 3x + 2y, 0) is linear.

A: The given function  is given by .To show that T is linear.

Q: Compute the discriminant D(x, y) of the function. ƒ(x, y) = x³ + y4 − 6x − 2y² + 2

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