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20. Determine which of the following set of functions is(are) linearly independent on (-∞, ∞). f₂(x)=x², f3(x) = 4x - 3x² f2(x) = cos²x, f(x) = sin²x f₂(x)=x-1, f3(x) = x+3 f₂(x) = e²¹, f3(x) = €¯² (A) fi(x)=x, (B) f(x) = 5, (C) fi(x) = x, (D) fi(x) = e,

20. Determine which of the following set of functions is(are) linearly independent on (-∞, ∞). f₂(x)=x², f3(x) = 4x - 3x² f2(x) = cos²x, f(x) = sin²x f₂(x)=x-1, f3(x) = x+3 f₂(x) = e²¹, f3(x) = €¯² (A) fi(x)=x, (B) f(x) = 5, (C) fi(x) = x, (D) fi(x) = e,

Calculus: Early Transcendentals
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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20. Determine which of the following set of functions is (are) linearly independent on (-∞, ∞). (A) fi(x)= x, f2(x) = x², f3(x) = 4x - 3x² (B) f(x) = 5, f2(x) = cos²x, f(x) = sin²x (C) f₁(x) = x, (D) fi(x)= e, f₂(x)=x-1, f₂(x) = e², f3(x)= x+3 f3(x) = e¯² 21. Which of the following statements is (are) true? (A) y = e is a solution of the DE y"+y' - 12y = 0. (B) y"-6y + 5y = -9 ln 2.x is a nonhomogeneous linear DE which can be solved by undetermined coefficients. (C) The roots of the auxiliary equation of the DE y" + 5y +6y= 0 are distinct imaginary. (D) The roots of the auxiliary equation of the DE y" + 3y" - 4y = 0 are both real and distinct. 22. Which of the following describes the nature of roots of the auxiliary equation corresponding to the DE y(4) + 3y" + 6y" + 5y+3y=0? (A) real - repeated; imaginary - distinct (B) real - distinct; imaginary - distinct (C) real - distinct; real-repeated; imaginary - distinct (D) imaginary repeated
Transcribed Image Text:20. Determine which of the following set of functions is (are) linearly independent on (-∞, ∞). (A) fi(x)= x, f2(x) = x², f3(x) = 4x - 3x² (B) f(x) = 5, f2(x) = cos²x, f(x) = sin²x (C) f₁(x) = x, (D) fi(x)= e, f₂(x)=x-1, f₂(x) = e², f3(x)= x+3 f3(x) = e¯² 21. Which of the following statements is (are) true? (A) y = e is a solution of the DE y"+y' - 12y = 0. (B) y"-6y + 5y = -9 ln 2.x is a nonhomogeneous linear DE which can be solved by undetermined coefficients. (C) The roots of the auxiliary equation of the DE y" + 5y +6y= 0 are distinct imaginary. (D) The roots of the auxiliary equation of the DE y" + 3y" - 4y = 0 are both real and distinct. 22. Which of the following describes the nature of roots of the auxiliary equation corresponding to the DE y(4) + 3y" + 6y" + 5y+3y=0? (A) real - repeated; imaginary - distinct (B) real - distinct; imaginary - distinct (C) real - distinct; real-repeated; imaginary - distinct (D) imaginary repeated
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