(a) k : R³→ R defined by: k (x) = x" Ax + b, %3D where: 3 -1 1 A = –1 3 1 1 1 -3 and b = 2. Is k (x) a quadratic form? (b) l : R²→ R defined by: 1(x) = x1e¬#1(x% – 4r2). Are any of the stationary points of l(x) global extrema? Why/why not?

Q: Suppose that f(x, y) = e−3x²—¹y²+6x+10y then find the discriminant of f. Submit Question

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Q: 2. Consider the following quadratic form; F(x,y) = ax? +2bxy + cy. Examine under which conditions on…

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Q: Find the point M(x,y) on the graph of f(x)=√x that is closest to A(a,0) where a is a positive real…

A: M(x,y)= (x,√x) Distance between (x, √x) and (a,0) is D.

Q: 17. Analyze the following quadratic function: f(x) =x* - 4x³ – 3x? +10x +8 12 pts Domain:…

A: From the given biquadratic function : f(x)=x4-4x3-3x2+10x+8 Being the polynomial function, domain is…

Q: = (15) Determine whether or not the functions y₁ 4x³, y2 = π, y3 = 12x², and y4 = 24x are linearly…

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Q: 3. Find the largest domain (in R2) for the function In(y-1) √x f(x, y): =

A: The given function fx,y=lny-1x We have to find the domain of fx,y

Q: 2. Given the parabola f(x) = -(x+ 2)² + 4, find the x-intercept(s). x = -2, x = 4 x = 4 x = 0, x =…

A: NOTE: Refresh your page if you can't see any equations. . to find the x-intercepts take f(x)=0

Q: Let y(t) be the solution of the IVP y = 2y- 3, y(1) = 2 then lim y(t) = Select one:

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Q: Find a quadratic function associated with vertex (h, k) = (1, 0) and point (x, y) = (–3, 4) that the…

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Q: z) = (x2 + then (a + E

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Q: Find the linearization L(x) of f(x) 5x2 5x + 5 at x х — 2. a) L(x) 15x 15 O b) L(x) 25x + 15 c) L(x)…

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Q: I. If f(x, y) = x² – y² + 4xy – 7x + 10, find (a) f(2, 1) (c) f(x + h, y) (b) f(-3, 5) (d) f(x, y +…

A: topic - functions note : As per bartleby guidelines, we are supposed to answer only first three…

Q: Determine whether linear or nonlinear:  y(t) = -jt*x (t) y(t) = j+x (t)

A: A linear equation is the one in which the highest degree is 1. A non-linear equation is an equation…

Q: 3.Find [, L (3x² + y)dydx

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Q: 1. Let f(x) = 3x + 1, g(x) = 7 – 2x, and h(x) = x² – 4.x + 5. Find the following: a) (f + g)(2) b)…

A: 1. Given, f(x)=3x+1g(x)=7-2xh(x)=x2-4x+5

Q: Classify each of the following quadratic forms: (a) Q(x, y, z) = 3y² + 4z² (b) Q(x, y, z) = (c) Q(x,…

A: We have to classify the given quadratic function.

Q: 6. A flying robot is programed to follow the following three-dimensional position function while…

A: Consider the equations xt=0.0560t4-1.200t2+2.300t+0.3400yt=0.6700t3-1.570t2zt=0.2200t3 Differentiate…

Q: 6 y = f(x) is the parabola shown. a Find f(3) and f'(3). b Hence find f (x) in the form f(x) = ax² +…

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Q: Find the constants c0, c1, and x1 so that the quadrature formula Z 1 0 f(x)dx = c0f(0) + c1f(x1),…

A: Consider the given quadrature formula, ∫01fxdx=c0f0+c1fx1 here we need to determine the constants…

Q: ind two linearly independent solutions of 2x²y" – xy' + (-5x + 1)y = 0, x > 0 of the form yı = x""…

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Q: ? ? ? 1. f(t) = 4t² + 28t, g(t) = 4t² - 28t 2. f(0) cos(30), = g(0) = -8 cos³ (0) + 6 cos (0) 3.…

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Q: C) Use the Chain rule to find () (). For the following functions: (1) u=xy-1 where: x = e-2r cos-1 r…

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

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Q: In C[0, 1], are the functions {x2 , x3 , e2x} linearly independent?

A: Linearly dependent and independent functions: Two differential functions f(x) and g(x) are said to…

Q: Write the equation of a cubic function, f(x), with zeros at -5, 0, and 2, and end behavior f(x)→ ∞…

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Q: Eliminate the Arbitrary Constant: y = c¿e* + c2xe* а. y — 2y" + 2у %3D 0 b.y" - 2y' + у %3D 0 c. y'…

A: y=c1ex+c2xex