15. Determine if the given functions are linearly dependent or independent. (Prove your answers) {e ,3x} b. (-9x +1,3x - c. (1-2 sin' x,cos 2x} с.
15. Determine if the given functions are linearly dependent or independent. (Prove your answers) {e ,3x} b. (-9x +1,3x - c. (1-2 sin' x,cos 2x} с.
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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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Q15. Onlys all the three subparts
![15. Determine if the given functions are linearly dependent or independent. (Prove your answers)
a. fe",3x} b. (-9x' +1,3x c. 1-2sin' x,cos 2.x}
16. Find the general solution to the given differential equations:
a. (D' + 2D+10) y = o
b. [D(D +4)]y =0
c. [(D +16)ly = 4cos.x
d. y" -y - 2y = Se
e. y" + 4y - 5y = 3sin 2r
17. Find an Annihilator Q(D) for the given functions:
a. F(x) - 3xe"
c. F(x) = e"+x
b. F(x) = 10
d. F(x) = - 6e" cos(5x)
e. F(x) = 1+7x-x
f. F(x) = sin x+ x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42899459-396d-4157-9621-538988e3c4d3%2Fd7218327-9f31-4d4e-a7a8-8358312f1ea4%2F1qwyzt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:15. Determine if the given functions are linearly dependent or independent. (Prove your answers)
a. fe",3x} b. (-9x' +1,3x c. 1-2sin' x,cos 2.x}
16. Find the general solution to the given differential equations:
a. (D' + 2D+10) y = o
b. [D(D +4)]y =0
c. [(D +16)ly = 4cos.x
d. y" -y - 2y = Se
e. y" + 4y - 5y = 3sin 2r
17. Find an Annihilator Q(D) for the given functions:
a. F(x) - 3xe"
c. F(x) = e"+x
b. F(x) = 10
d. F(x) = - 6e" cos(5x)
e. F(x) = 1+7x-x
f. F(x) = sin x+ x
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