1. A function f(x, y) is homogeneous of degree 7 in x and y if and only if,2. The function f(x, y)= 5x' -2y'8x+3yis homogenous in x and y of degree.

We have to find degree of homogeneous function

Answered: 1. A function f(x, y) is homogeneous of…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Check if the system with the following input-output relation are i) Memory/memory lessii) Causal /non-causala) y(t) =x^4(t) + x(t-3) b) y(n) = x(n-2) +3y(n-1)c) y(t) = A cos (2ㅠft + x(t))
8) Rectangle GHJK with vertices G(2,3), H(2, 5), J(6, 5) and K(6, 3) is rotated 180° about the origin to make rectangle G'H'J’K'. -2 -3 F (x, y)→(-x, y) G (x, y) →(-x, -y) H (х, у) —> (-у, х) J (х, у) > (у, -х)
6. Let A € R"хп, х, b E R, Q(х) — || Ах — b|Е. (a) Find the gradient of Q(x). (b) When there is a unique stationary point for Q(x). (Hint: stationary point is where gradient equals to zero)
Please give the number 1 answer! Thank you!
5. (a) Let f(x) and g(x) be smooth functions from R to R, show that if f(x) and g(x) have contact of order n at p then f(x) and g(x) are k-th order of approximations of one another for all k = 1, 2, ..., n. (b) Let f(x1,...,xm) and g(x₁, ..., xm) be smooth functions from Rm to R, what role does T(f), the n-th Taylor polynomial of a function f centered at the point p, play in this topic of k-th order approximation?
Find f, f, and f, and evaluate each at the given point. x'y' z' xy f(x, y, z) = (4, 1, –1) x+y+z f,(X, y, z) fy(x, Y, Z) ,Y, 2 (X, Y, z) f,(4, 1, -1) (4, 1, -1) f,(4, 1, -1)
1 1. Let f (x) = x² - 5, g (x) = V5 - x and h (x) 2x - 1' a) Determine the domain of f, g and h. b) Find (h ofog)(x).
5. (a) Let f(x) and g(x) be smooth functions from R to R, show that if f(x) and g(x) have contact of order n at p then f(x) and g(x) are k-th order of approximations of one another for all k = 1, 2,..., n. (b) Let f(x1,...,m) and g(x1, ..., xm) be smooth functions from Rm to R, what role does T(f), the n-th Taylor polynomial of a function f centered at the point p, play in this topic of k-th order approximation?
5. The function g(x) is continuous on the closed interval [-2, 0] and twice differentiable on the open interval (-2, 0). If g'(-1)=-2 and g"(x) > 0 on the open interval (-2, 0), which of the following could be a table of values of g? X -2 -1 0 A. g(x) 5 3 1 X -2 -1 0 B. g(x) 5 4 1 Y -2 -1 0 C. g(x) 5 6 9 D. X -2 -1 0 g(x) 5 7 9 X 1-2 -1 0 E. g(x) 7.5 4 3.5
Use Wronskian

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1. A function f(x, y) is homogeneous of degree 7 in x and y if and only if, 2. The function f(x, y)= X-29 is homogenous in x and y of degree &r+3y