(c) Consider R² with the norm ||x|| = \5i| + I52| for any x = (§1,52) € R². Let y = (1, 1) e R² and find a linear functional f which has norm 1 and satisfies f(y) = llyll. Justify your answer. %3D %3D %3D

Q: 3. Find the fixed point(s) of f : [1, 0) → [2, 0) defined by f(x) = vx² + x.

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Q: -If fand g are two scalar point functions then prove that div (fV g) =fV° g+Vf- Vg

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Q: 3. Compute the value of F.dr if F = -yi + xj and C is a semicircle from (-1,1) to (1,-1).

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Q: For the following graphical figure, write the function x(n) and h(n) in: 1. sequential vector 2.…

A: 1) Sequential representation x( n)= {0,0,0,1,2,3,1,0,0}    ↑ The time origin (n=0)(x(0)=1) is…

Q: In(1 – a2 – y?) - Consider f (æ, y) %3D (a) Determine the domain of f(x, y) and sketch the domain on…

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Q: 5. Express the given function using unit step function: * [t f (t) = 0st<4 2 , t24 O A.) f (t) = t…

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Q: Let (x, y) eRx R. Consider the following functions from R? to R? r((x, y)) = (-y, x) and s(x, y)) =…

A: This is a problem of multivariable Calculus.

Q: 2. Show that e*, sin x, cos x are linearly independent using Wronskian Method.

A: As per the policy of bartleby the provisions is to solve only one question at a time  I am solving…

Q: Let F(x, y) = (x¹7e², 7) and C be the path along the right half of the circle (r - 3)² + (y – 5)² =…

A: 28.2) To evaluate the line integral ∫CF.dr for the function F(x,y)=(x17ex2,7) where C is the right…

Q: Another derivative combination Let F = (f. g, h) and let u be a differentiable scalar-valued…

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Q: Graph the functions in Exercises 39 to 56

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the linear approximation of the function at the given point. ffx y)=-9x2-6y2+ 6 at (6,-10)…

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Q: 8 (1) = {(In(3-1) 141-13, 38²2-8), t), ‚31² t (0,−1, 4), t . Find the domain of Ř.

A: This is a problem of vector calculus.

Q: Consider the vector-valued function F(t) = exists. 21-6 In(-2) ²³-2t, 2-4t+3/ Find lim F(t), if it…

A: Here we have to find limit of given vector valued function.

Q: please show steps

A: We apply rule of linearly independent of sets

Q: Compute Fx, fy, and fz for the function and evaluate them at the indicated points

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Q: please see image

A: Taking the cues from hint in the question:

Q: 3.2. Show, using the two properties that define a linear function, whether each of the following…

A: Solution: (3.2) Functions are linear: (i) fx1;x2=5x1+lne6x2 Now, fx1+y1;x2+y2=5x1+y1+lne6x2+y2…

Q: Ques. 3: Check whether the operator T: R2 → R² defined by T(x,y) = (y,x) is linear. Moreover if T is…

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Q: let T: P4→ P3 be defined by T(p) = p'. what is the kernel of T? The set of quadratic functions. El…

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Q: Let L: R2 → R2² be the linear operator defined by L 2

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Q: Which of the following subsets of functions of the set {eª, e²ª, 2eª, 2} is linearly dependent on R?…

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Q: The table below lists the height h (in cm), the age a (in years), the gender g (1="Male",…

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Q: 5. Given f(x) = -2/4x – 8 +1 a. Determine the parent function b. Determine the mapping rule c. Map…

A: Given function

Q: 2. Let f= L(X,Y). Show that ƒ is one to one iff (f(x).(x)....(x)) is linear independent when (x,x)…

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Q: E.g. Let f(x, y) = x² - 2xy + y². The graph and contour diagram of f is given below right. Compute…

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Q: the degree of homogeneity, if there is one, for eac 1 X1,X2, X3) = - xf +x +x X2 X3 O gro finotion:…

A: Introduction: For a function f(x,y), the degree of homogeneity is an integer n such that,…