(1) Let G: R → R? be a differentiable function such that G(1, -1,3) = (2,5) and DG(1, –1,3) = 1 -1 4 0 7 Suppose that F: R? R? is defined by F(r,y) = (2ry, 3r-y+5). What is D(F o G)(1,-1,3)? %3D

Q: 2. Find and classify all the extrema of the function f(s, t) = (4s² + 2t²)e¯

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Q: The range of the function f (x, y) = 4 – 4 – x² – y² i - [2, 00) (-0, 4 (-∞0, 2 [4, 0) [2, 4]

A: Here, the given function is: f(x,y)=4-4-x2-y2 Here, the maximum value of 4-x2-y2 is 4=2 and minimum…

Q: Suppose f is a differentiable function of x and y, and g(r, s) = f(2rs, s² - 6r). Use the table of…

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A: Given F(u,v)be a function of two variables. let Fu(u,v)=G(u,v) and Fv(u,v)=H(u,v) Here f(x)=F(u,v)…

Q: if (x, y) ± (0,0) x6 + y6 Let f(x, y) if (x, y) = (0,0) if (æ, y) + (0,0) and let g(x, y) 6x10 +…

A: Introduction: In multivariable calculus, the limit of a function can also be determined. The limit…

Q: Which of the following statements are false? ) The domain of the function f(z, y, z) = + sin-(z + y)…

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Q: 1. Given that f is the function defined by f(x, y) = 2¹+y²-²-2y, determine the relative extrema of f…

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Q: (2) I Let (x, y) E R X R. Consider the following functions from R? to R? r((x, y)) = (-y, x) and…

A: We have to find the order of r and s. Here rx, y=-y, x and sx, y=x, -y where x, y∈ℝ. First, we have…

Q: Consider the three points (2, 4), (4, 6), and (-2,7). (a) Supposed that at (2,4), we know that f₂z =…

A: Let us consider the given function f(x,y) and (a,b) is critical point then fx=fy=0. Determine…

Q: Suppose f is a differentiable function of x and y, and g(r, s) = f(2r – s, s - 3r). Use the table of…

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Q: Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find (1) and s'(4). y…

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Q: Let F(x, y) =. Evaluate (31) F dr (1,0,0) O a. 9 + 3e3 8+ 3e3 С. 8— Зе3 O d. 10 – 3e3

A: We will use basic knowledge of vector calculus and integral calculus to answer this question.

Q: 10. Let F(x, y, z)= y-yz+1 £z+r-z z+xy-y Find a function g such that F = √g.

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Q: 1. Let f(x, y): x-y x+y+1 Find:

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Q: The gradient of the lcalar function f= x²+y2+z²is. fa) xityj+zk tyjt +龙ん

A: Gradient of a function fx, y, z is given by  gradf=∂f∂xi+∂f∂yj+∂f∂zk

Q: Determine a potential function to evaluate (F*dR for C any path from the first point to the second.…

A: Given:F=3x2(y2−4y)i^+(2x3y−4x3)j^​Two points: (x1, y1) = (-1, 1)(x2, y2) = (2, 3)To determine a…

Q: Z is the set of integers, R is the set of real mumbers. 1. Functions f, 9, and h are defined as f:R…

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Q: Exercise 1. A student is asked to prove If m is even and n is odd, then m² + n² is odd. 2 The…

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Q: The range of the function f(x, y) = 6 – /4 – 2² – y?is O [4, 6] O [4, 0) 0 (-0, 4] 0(-0, 6| O (6,…

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Q: or the function, evaluate the following. (If an answer does not exist, enter DNE.) д(x, у, 2) In(x +…

A: Put value in function

Q: Consider the functions f, g given by f(y) = Ay, g(x) = Bx where A is m × p and B is p × n. In…

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Q: Suppose f is a differentiable function of x and y and g(u, v) = f(2u – v, v² – 4u). Use the table of…

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Q: (x +1)4 – y² Let f(x, y) = { (x + 1)4 + y? - if (x, y) # (–1,0) -1 if (x, y) = (-1,0) a. Show that f…

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Q: The approximated value for e using the Maclaurin series expansion coasidering a true relative error…

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Q: The function, f(x), in the graph below has f(1) = 1 and f'(1) = 2. Which of the following are the…

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Q: (i) Find domain and range of the following functions f(x, y, z) = /x – y² and g(x, y, z) = V1-x² yz…

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Q: (a) f(2, 1, 2) (b) f(-3, 2, 1) (c) f(0, 0, 0) (e) f(t, 1², –t) (d) f(a, a, a) (f) f(a +b, a – b, b).…

A: Given: The function f(x,y,z)=xy2z3+3 where f is a function of x, y, and z. To find: f(2,1,2),…

Q: Determine the value of m such that the function x- y - 5 E + 5 VI - Vỹ f(x, y) = is continuous at…

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