Let n N and Me Rnxn. Consider the function f R" → R defined by f(x) = (x, Mx) for all x € R". i) Provide an argument that f is twice continuously differentiable. ii) Compute the gradient and the Hessian of f.

Q: Let T be function from R to R defined as T (z) = (r, x), %3D Then T is not linear operator O True…

A: FALSE  the detailed explanation is as follows below:

Q: Let f : R R:f(x) = 10x + 7. Find the function g : R→R such that gof = fog = IR. %3D %3D

A: Given f: R -> R  such that f(x) = 10x + 7 and  g : R -> R such that g o f = f o g = IR

Q: f: R2 → R, f(x1, x2) = x1-x2 function is given. a) Can f be an surjective function? b) Can f be an…

A:

Q: p+q Consider the function f(p, q, r) = w = 2. af with p = v²w³ + u, q = w³ + v², and r = uv³ + 1.…

A:

Q: Consider the triangle AABC Where Ã= 0 B= and C= 1 Find the coordinates of the vertices of the dual…

A: Consider the triangle ∆ ABC and

Q: Show that the operator U is positive U: 1² ([0,1]) → L²([0,1]), Uƒ (x) = X[{0,1] [~*\f(t)\dt

A: To show that the operator U is positive, need to demonstrate that for any f∈L2([0,1]), the inner…

Q: f(x, y) = x² + y² +1 f (x, y)

A: Let's find.

Q: analytic function a domain D. If a zeck. y) + b v(x, y) = C in D are real Constants not all o. #2.…

A: If f(z)=u+iv is analytic in a domain D , then f satiesfies the Cauchy Riemann (C-R) equations that…

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A: It is given that, x,y,z are a function of the independent variables u,v,w. Here we have to find…

Q: Check the differentiability of the function f(x, y) = √xy | at the point (0,0). Also check the…

A: As per the question we are give a bivariate function : f(x,y) = √|xy| And we have to check for its…

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A: Here in the given question, there are 4 observations and the cost in dollars V is decreasing and…

Q: Give an interval over which the set of two functions fi(x) = x² and f2(x) = x |x| is linearly…

A: Given: The set of two function.f1(x)=x2f2(x)=xx

Q: Define f : R 2 → R by f(x, y) = x 2 + y 2 . Compute the linearization of f at (−1, 1).

A: We have to find the linearlization at (-1, 1)

Q: 15.8 Consider the equation x³ + 3y² + 4xz² – 3z²y = 1. Does this equation define z as a function of…

A: Given:  The equation: x3 + 3y2 + 4xz2 - 3z2y = 1. To define: z in the equation as a function of x…

Q: Let f = f(x,y, z) be a sufficiently smooth scalar function and F = Vƒ be the gradient acting on f.…

A:

Q: Suppose X1, X2 ∼ Unif(0, 1) and are independent. Let Y = min(X1, X2). Find fY (y).

A: We have given that X1,X2∼U(0,1)Objective :To find the  PDF of Y=min(X1,X2)

Q: Let V = span{e2", xe2", x²e?=}. (a) Show that (a1e2a + a2xe2" + a3x²e2") e V for any a1, a2, az E R,…

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

A:

Q: Consider the function ƒ (x, y, z) = 2x² + 5y² + z². a) If ƒ (x, y, z) is the profit made from…

A:

Q: Let h : R → R be some twice-differentiable function. Define f(x,y) = h(x) for all x ≠ 0. Show that…

A:

Q: Let F(x, y, z) = (14xyz + 7sin(x))i + 7x²zj + 7x²yk. Find a function f such that F = Vf. f(x, y, z)…

A:

Q: b) Let f: D→ C be a function and Y a subset of C. Show that f¹ [C-Y] =D-f¹ [Y].

A:

Q: Let f: R2 R2 be the function given by f(x, y) = (x + y, y). Prove or →>> 8. disprove: f is…

A: Function which is one to one

Q: A = [a,b), be an (right half-open) interval of R. 6 (c) (d) a,be R+,b+00, Explain whether f(A) is…

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Q: f: R2 → R, f(x1, x2) = x1-x2 function is given. a) Can f be an surjective function? b) Can f be an…

A: f: R2 → R, f(x1, x2) = x1-x2 function is given. a) Can f be an surjective function? b) Can f be an…

Q: Qs, find Thi domain of He function

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Q: Find f, and f, for f(x,y)=y In (3x +4y). fx fy

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: Find the gradient function for: 1+3x 1) y = %3D x2 +1

A: Given that  y=(1+3x)/(x^2+1) To find the gradient of y

Q: |. consider the function f defined by f(x) x€ (-1,1). 3 Vin Cl+z)-Sec (x) a) Find linearteation of f…

A: Definition: Let f(x) be differentiable function on the given domain. The linearization L(x) of f(x)…