7 → V by a(f)(x) = x² ƒ"(x), where ƒ" (x) is the double differential of a polynomial f(x). pjection? re exist a subspace WCV of V such that V = Im(a) + W?

Q: u(0,1)= 0, U(1,1)=0, u(x,0)=2x u(x,0)=2 ALE. A Q.4/Answer ONLY TWO, Except (C) (4) Using Lagrange…

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Q: Question 4 Find the gradient of the function at the given point. w = 2x - 4yz+z², (1, 1, −2) 21+…

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Q: Let F(x,y,z) = (x)i + (y)j + (z2)k. Compute the defined operations and if it is not defined, write…

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Q: Q1] (A) If F(x+y-2₁x² + y²)=0 where z=2(x, y) and дz дz -у-=х-у ду ах - 0 then prov

A: (.)  Leibniz rule :      Given ,(A).        where   and   .

Q: ind positive constants b and n, such that 3n + 2 n.

A: Finding the values of b and no

Q: f(1, 1) = f₁(1)f₂(1) f(1, 2) # f₁(1)f₂ (2) for x = 1, y = 1,2 then x and y are: dependent O…

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Q: Find and classify the stationary point(s) of the following functions: (a) 1: R³→ R defined by: 1(x)…

A: As per Bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: of the form y₁ = (1+₁2+ a₂x² + 3x³ + ...) 32 = x2(1+b₁x + b₂x² + b₂x³ + ...) where T₁ > T2- Enter…

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Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: Suppose z = x + iy and f(z) = z - 1. Find w = u + iv such that f(w) = 1 + 3i (A) 3+2i (B) 3-2i (C)…

A: We have given that , fz = z - 1 , where , z = x + iy Here , w = u + iv Let , fw = 1 + 3i We need to…

Q: What is the length of EF? y 4 8 units 10- 7 units 4 2 units -10 -8 -6 4 10x -2- 6 units -4- -6 -8

A: solution of the given problem is below ...

Q: = 0. c) y(0) = 1, y'(0) = 0, y"(0) = -1. Is the set of functions linearly independent or linearly…

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Q: -3t k Compute the first, second, and third derivatives of r(t) = 3ti + 5 In(t)j + 5e

A: r(t)=(3t)i+(5lnt)j+(5e-3t)k   We are required to findFirst derivative Second derivativeThird…

Q: Let f(x,y) = x - 4xy - y. Compute f(4,0) and f(4, – 4). f(4,0) = (Simplify your answer.)

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Q: f (x, y) ~ bo + b1,0(x − 1)+b0,1(y−2)+ b2,0 (x - 1)² + b₁,1(x − 1)(y-2) + bo,2(y − 2)² +…...

A: We find the Taylor series of the given function

Q: Discuss the continuity of the function 2ху +y? f(x.y): (x, y) # (0,0)

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Q: (x + 3)³ 12 16 11 f(x) Consider the function 4(х — 1)2 4 1 (x – 1)2 4. Note that - (x – 9)(x + 3)²…

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Q: f(x,y) = –x² + 2xy + 3y² – 6x – 2y – 4 | - Serialize the function around the point (-2,1). a) f(x,y)…

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Q: Let (G (1,-1,i,-i),.) then Evagcent ()[G:c(a)] = 2 3 1

A: We will use the following results i) Any group of order 4 is abelian group. ii) Every element of…

Q: dependent.

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Q: f(1, 1) = f₁(1)f₂(1) f(1, 2) # f₁(1)f₂(2) for x = 1, y = 1,2 then x and y are: dependent O…

A: Since we know that  If x and y are independent the it must satisfy the following condition f(x,y) =…

Q: 3 is the imagina u =

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Q: 17. Let y₁ = x₁ + x₂ and y₂ = x² + x² + 2(x₁ + x₂ + x₁x₂). (a) Use the Jacobian to test whether…

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Q: (b) By determining constants c,, C2, C3 and c4, which are not all zero and are such that cifi(x) +…

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Q: Given f(x, y) and y = y(x), we can define a composite functiong(x) = f(x,y(x)).

A: a)Given , gx=fx,yx Then, g'x=∂f∂x+∂f∂yddxyx  [∵y=yx]⇒g'x=∂f∂x+∂f∂yy'x