Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Question
Chapter 3.1, Problem 17E
To determine
Whether the set of functions
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In Problems 11–20, for the given functions f and g. find:
(a) (f° g)(4)
(b) (g•f)(2)
(c) (fof)(1)
(d) (g ° g)(0)
\ 11. f(x) = 2x; g(x) = 3x² + 1
12. f(x) = 3x + 2; g(x) = 2x² – 1
1
13. f(x) = 4x² – 3; g(x) = 3
14. f(x) = 2x²; g(x) = 1 – 3x²
15. f(x) = Vx; 8(x) = 2x
16. f(x) = Vx + 1; g(x) = 3x
%3D
1.
17. f(x) = |x|; g(x) =
18. f(x) = |x – 2|: g(x)
x² + 2
2
x + 1
x² + 1
19. f(x) =
3
8(x) = Vĩ
20. f(x) = x³/2; g(x) =
X + 1'
10. Find all the numbers for which f (x)<0 if f (x)= x* + 2x' – 7x² – 8x+12.
b. (-∞,-2)U(1,2).
(-2,1)U(2,0).
(-3,–2)U(1,2).
c.
(-0,–3)U(1,2).
а.
d. (-2,1)U(1,2).
е.
(12) If y = a X"-b X*+1 +5 is a polynomial and a s bER* , then
d" y
may by represent
dX"
by one of the following figures
(b)
().
Chapter 3 Solutions
Advanced Engineering Mathematics
Ch. 3.1 - Prob. 1ECh. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10E
Ch. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Prob. 40ECh. 3.1 - Prob. 42ECh. 3.2 - Prob. 1ECh. 3.2 - Prob. 2ECh. 3.2 - Prob. 3ECh. 3.2 - Prob. 4ECh. 3.2 - Prob. 5ECh. 3.2 - Prob. 6ECh. 3.2 - Prob. 7ECh. 3.2 - Prob. 8ECh. 3.2 - Prob. 9ECh. 3.2 - Prob. 10ECh. 3.2 - Prob. 11ECh. 3.2 - Prob. 12ECh. 3.2 - Prob. 13ECh. 3.2 - Prob. 14ECh. 3.2 - Prob. 15ECh. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.2 - Prob. 18ECh. 3.2 - Prob. 19ECh. 3.2 - Prob. 20ECh. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Prob. 10ECh. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 - Prob. 17ECh. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - Prob. 24ECh. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Prob. 29ECh. 3.3 - Prob. 30ECh. 3.3 - Prob. 31ECh. 3.3 - Prob. 32ECh. 3.3 - Prob. 33ECh. 3.3 - Prob. 34ECh. 3.3 - Prob. 35ECh. 3.3 - Prob. 36ECh. 3.3 - Prob. 37ECh. 3.3 - Prob. 38ECh. 3.3 - Prob. 39ECh. 3.3 - Prob. 40ECh. 3.3 - Prob. 41ECh. 3.3 - Prob. 42ECh. 3.3 - Prob. 43ECh. 3.3 - Prob. 44ECh. 3.3 - Prob. 45ECh. 3.3 - Prob. 46ECh. 3.3 - Prob. 47ECh. 3.3 - Prob. 48ECh. 3.3 - Prob. 49ECh. 3.3 - Prob. 50ECh. 3.3 - Prob. 51ECh. 3.3 - Prob. 52ECh. 3.3 - Prob. 53ECh. 3.3 - Prob. 54ECh. 3.3 - Prob. 55ECh. 3.3 - Prob. 56ECh. 3.3 - Prob. 57ECh. 3.3 - Prob. 58ECh. 3.3 - Prob. 59ECh. 3.3 - Prob. 60ECh. 3.3 - Prob. 61ECh. 3.3 - Prob. 62ECh. 3.3 - Prob. 63ECh. 3.4 - Prob. 1ECh. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - Prob. 5ECh. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Prob. 22ECh. 3.4 - Prob. 23ECh. 3.4 - Prob. 24ECh. 3.4 - Prob. 25ECh. 3.4 - Prob. 26ECh. 3.4 - Prob. 27ECh. 3.4 - Prob. 28ECh. 3.4 - Prob. 29ECh. 3.4 - Prob. 30ECh. 3.4 - Prob. 31ECh. 3.4 - Prob. 32ECh. 3.4 - Prob. 33ECh. 3.4 - Prob. 34ECh. 3.4 - Prob. 35ECh. 3.4 - Prob. 36ECh. 3.4 - Prob. 37ECh. 3.4 - Prob. 38ECh. 3.4 - Prob. 39ECh. 3.4 - Prob. 40ECh. 3.4 - Prob. 41ECh. 3.4 - Prob. 42ECh. 3.4 - Prob. 43ECh. 3.4 - Prob. 44ECh. 3.4 - Prob. 45ECh. 3.4 - Prob. 46ECh. 3.4 - Prob. 47ECh. 3.4 - Prob. 48ECh. 3.5 - Prob. 1ECh. 3.5 - Prob. 2ECh. 3.5 - Prob. 3ECh. 3.5 - Prob. 4ECh. 3.5 - Prob. 5ECh. 3.5 - Prob. 6ECh. 3.5 - Prob. 7ECh. 3.5 - Prob. 8ECh. 3.5 - Prob. 9ECh. 3.5 - Prob. 10ECh. 3.5 - Prob. 11ECh. 3.5 - Prob. 12ECh. 3.5 - Prob. 13ECh. 3.5 - Prob. 14ECh. 3.5 - Prob. 15ECh. 3.5 - Prob. 16ECh. 3.5 - Prob. 17ECh. 3.5 - Prob. 18ECh. 3.5 - Prob. 19ECh. 3.5 - Prob. 20ECh. 3.5 - Prob. 21ECh. 3.5 - Prob. 22ECh. 3.5 - Prob. 23ECh. 3.5 - Prob. 24ECh. 3.5 - Prob. 25ECh. 3.5 - Prob. 26ECh. 3.5 - Prob. 27ECh. 3.5 - Prob. 28ECh. 3.5 - Prob. 29ECh. 3.5 - Prob. 30ECh. 3.5 - Prob. 31ECh. 3.5 - Prob. 32ECh. 3.5 - Prob. 33ECh. 3.5 - Prob. 34ECh. 3.6 - Prob. 1ECh. 3.6 - Prob. 2ECh. 3.6 - Prob. 3ECh. 3.6 - Prob. 4ECh. 3.6 - Prob. 5ECh. 3.6 - Prob. 6ECh. 3.6 - Prob. 7ECh. 3.6 - Prob. 8ECh. 3.6 - Prob. 9ECh. 3.6 - Prob. 10ECh. 3.6 - Prob. 11ECh. 3.6 - Prob. 12ECh. 3.6 - Prob. 13ECh. 3.6 - Prob. 14ECh. 3.6 - Prob. 15ECh. 3.6 - Prob. 16ECh. 3.6 - Prob. 17ECh. 3.6 - Prob. 18ECh. 3.6 - Prob. 19ECh. 3.6 - Prob. 20ECh. 3.6 - Prob. 21ECh. 3.6 - Prob. 22ECh. 3.6 - Prob. 23ECh. 3.6 - Prob. 24ECh. 3.6 - Prob. 25ECh. 3.6 - Prob. 26ECh. 3.6 - Prob. 27ECh. 3.6 - Prob. 28ECh. 3.6 - Prob. 29ECh. 3.6 - Prob. 30ECh. 3.6 - Prob. 31ECh. 3.6 - Prob. 32ECh. 3.6 - Prob. 33ECh. 3.6 - Prob. 34ECh. 3.6 - Prob. 35ECh. 3.6 - Prob. 36ECh. 3.6 - Prob. 37ECh. 3.6 - Prob. 38ECh. 3.6 - Prob. 39ECh. 3.6 - Prob. 40ECh. 3.6 - Prob. 41ECh. 3.6 - Prob. 42ECh. 3.6 - Prob. 43ECh. 3.6 - Prob. 44ECh. 3.6 - Prob. 45ECh. 3.6 - Prob. 46ECh. 3.6 - Prob. 47ECh. 3.6 - Prob. 48ECh. 3.6 - Prob. 49ECh. 3.6 - Prob. 50ECh. 3.6 - Prob. 51ECh. 3.6 - Prob. 52ECh. 3.6 - Prob. 55ECh. 3.6 - Prob. 56ECh. 3.6 - Prob. 57ECh. 3.7 - Prob. 1ECh. 3.7 - Prob. 2ECh. 3.7 - Prob. 3ECh. 3.7 - Prob. 4ECh. 3.7 - Prob. 5ECh. 3.7 - Prob. 6ECh. 3.7 - Prob. 7ECh. 3.7 - Prob. 8ECh. 3.7 - Prob. 9ECh. 3.7 - Prob. 10ECh. 3.7 - Prob. 11ECh. 3.7 - Prob. 12ECh. 3.7 - Prob. 13ECh. 3.7 - Prob. 14ECh. 3.7 - Prob. 15ECh. 3.7 - Prob. 16ECh. 3.7 - Prob. 17ECh. 3.7 - Prob. 18ECh. 3.7 - Prob. 19ECh. 3.7 - Prob. 20ECh. 3.7 - Prob. 21ECh. 3.7 - Prob. 22ECh. 3.7 - Prob. 23ECh. 3.8 - Prob. 1ECh. 3.8 - Prob. 2ECh. 3.8 - Prob. 3ECh. 3.8 - Prob. 4ECh. 3.8 - Prob. 5ECh. 3.8 - Prob. 6ECh. 3.8 - Prob. 7ECh. 3.8 - Prob. 8ECh. 3.8 - Prob. 9ECh. 3.8 - Prob. 10ECh. 3.8 - Prob. 11ECh. 3.8 - Prob. 12ECh. 3.8 - Prob. 13ECh. 3.8 - Prob. 14ECh. 3.8 - Prob. 15ECh. 3.8 - Prob. 16ECh. 3.8 - Prob. 17ECh. 3.8 - Prob. 18ECh. 3.8 - Prob. 19ECh. 3.8 - Prob. 20ECh. 3.8 - Prob. 21ECh. 3.8 - Prob. 22ECh. 3.8 - Prob. 23ECh. 3.8 - Prob. 24ECh. 3.8 - Prob. 25ECh. 3.8 - Prob. 26ECh. 3.8 - Prob. 27ECh. 3.8 - Prob. 28ECh. 3.8 - Prob. 29ECh. 3.8 - Prob. 30ECh. 3.8 - Prob. 31ECh. 3.8 - Prob. 32ECh. 3.8 - Prob. 33ECh. 3.8 - Prob. 34ECh. 3.8 - Prob. 35ECh. 3.8 - Prob. 36ECh. 3.8 - Prob. 37ECh. 3.8 - Prob. 38ECh. 3.8 - Prob. 39ECh. 3.8 - Prob. 41ECh. 3.8 - Prob. 42ECh. 3.8 - Prob. 43ECh. 3.8 - Prob. 44ECh. 3.8 - Prob. 45ECh. 3.8 - Prob. 49ECh. 3.8 - Prob. 50ECh. 3.8 - Prob. 51ECh. 3.8 - Prob. 52ECh. 3.8 - Prob. 53ECh. 3.8 - Prob. 54ECh. 3.8 - Prob. 55ECh. 3.8 - Prob. 56ECh. 3.8 - Prob. 57ECh. 3.8 - Prob. 58ECh. 3.8 - Prob. 59ECh. 3.8 - Prob. 60ECh. 3.8 - Prob. 61ECh. 3.8 - Prob. 62ECh. 3.9 - Prob. 1ECh. 3.9 - Prob. 2ECh. 3.9 - Prob. 3ECh. 3.9 - Prob. 4ECh. 3.9 - Prob. 6ECh. 3.9 - Prob. 7ECh. 3.9 - Prob. 8ECh. 3.9 - Prob. 11ECh. 3.9 - Prob. 12ECh. 3.9 - Prob. 13ECh. 3.9 - Prob. 14ECh. 3.9 - Prob. 15ECh. 3.9 - Prob. 16ECh. 3.9 - Prob. 17ECh. 3.9 - Prob. 18ECh. 3.9 - Prob. 19ECh. 3.9 - Prob. 20ECh. 3.9 - Prob. 21ECh. 3.9 - Prob. 22ECh. 3.9 - Prob. 23ECh. 3.9 - Prob. 24ECh. 3.9 - Prob. 25ECh. 3.9 - Prob. 27ECh. 3.9 - Prob. 28ECh. 3.9 - Prob. 29ECh. 3.9 - Prob. 30ECh. 3.9 - Prob. 31ECh. 3.9 - Prob. 32ECh. 3.9 - Prob. 33ECh. 3.9 - Prob. 34ECh. 3.9 - Prob. 35ECh. 3.9 - Prob. 36ECh. 3.9 - Prob. 37ECh. 3.9 - Prob. 38ECh. 3.10 - Prob. 1ECh. 3.10 - Prob. 2ECh. 3.10 - Prob. 3ECh. 3.10 - Prob. 4ECh. 3.10 - Prob. 5ECh. 3.10 - Prob. 6ECh. 3.10 - Prob. 7ECh. 3.10 - Prob. 8ECh. 3.10 - Prob. 9ECh. 3.10 - Prob. 10ECh. 3.10 - Prob. 11ECh. 3.10 - Prob. 12ECh. 3.10 - Prob. 13ECh. 3.10 - Prob. 14ECh. 3.10 - Prob. 15ECh. 3.10 - Prob. 16ECh. 3.10 - Prob. 17ECh. 3.10 - Prob. 18ECh. 3.10 - Prob. 19ECh. 3.10 - Prob. 20ECh. 3.10 - Prob. 21ECh. 3.10 - Prob. 22ECh. 3.10 - Prob. 23ECh. 3.10 - Prob. 24ECh. 3.10 - Prob. 25ECh. 3.10 - Prob. 26ECh. 3.10 - Prob. 27ECh. 3.10 - Prob. 28ECh. 3.10 - Prob. 29ECh. 3.10 - Prob. 30ECh. 3.10 - Prob. 31ECh. 3.10 - Prob. 32ECh. 3.10 - Prob. 33ECh. 3.10 - Prob. 34ECh. 3.10 - Prob. 35ECh. 3.10 - Prob. 36ECh. 3.10 - Prob. 37ECh. 3.10 - Prob. 38ECh. 3.10 - Prob. 39ECh. 3.10 - Prob. 40ECh. 3.10 - Prob. 41ECh. 3.10 - Prob. 42ECh. 3.10 - Prob. 43ECh. 3.10 - Prob. 44ECh. 3.10 - Prob. 45ECh. 3.10 - Prob. 46ECh. 3.11 - Prob. 7ECh. 3.11 - Prob. 14ECh. 3.11 - Prob. 15ECh. 3.11 - Prob. 16ECh. 3.11 - Prob. 20ECh. 3.11 - Prob. 21ECh. 3.12 - Prob. 1ECh. 3.12 - Prob. 2ECh. 3.12 - Prob. 3ECh. 3.12 - Prob. 4ECh. 3.12 - Prob. 5ECh. 3.12 - Prob. 6ECh. 3.12 - Prob. 7ECh. 3.12 - Prob. 8ECh. 3.12 - Prob. 9ECh. 3.12 - Prob. 10ECh. 3.12 - Prob. 11ECh. 3.12 - Prob. 12ECh. 3.12 - Prob. 13ECh. 3.12 - Prob. 14ECh. 3.12 - Prob. 15ECh. 3.12 - Prob. 16ECh. 3.12 - Prob. 17ECh. 3.12 - Prob. 18ECh. 3.12 - Prob. 19ECh. 3.12 - Prob. 20ECh. 3.12 - Prob. 21ECh. 3.12 - Prob. 22ECh. 3.12 - Prob. 23ECh. 3.12 - Prob. 24ECh. 3 - Prob. 1CRCh. 3 - Prob. 2CRCh. 3 - Prob. 3CRCh. 3 - Prob. 4CRCh. 3 - Prob. 5CRCh. 3 - Prob. 6CRCh. 3 - Prob. 7CRCh. 3 - Prob. 8CRCh. 3 - Prob. 9CRCh. 3 - Prob. 10CRCh. 3 - Prob. 11CRCh. 3 - Prob. 12CRCh. 3 - Prob. 13CRCh. 3 - Prob. 14CRCh. 3 - Prob. 15CRCh. 3 - Prob. 16CRCh. 3 - Prob. 17CRCh. 3 - Prob. 18CRCh. 3 - Prob. 19CRCh. 3 - Prob. 20CRCh. 3 - Prob. 21CRCh. 3 - Prob. 22CRCh. 3 - Prob. 23CRCh. 3 - Prob. 24CRCh. 3 - Prob. 25CRCh. 3 - Prob. 26CRCh. 3 - Prob. 27CRCh. 3 - Prob. 28CRCh. 3 - Prob. 29CRCh. 3 - Prob. 30CRCh. 3 - Prob. 31CRCh. 3 - Prob. 32CRCh. 3 - Prob. 33CRCh. 3 - Prob. 34CRCh. 3 - Prob. 35CRCh. 3 - Prob. 36CRCh. 3 - Prob. 37CRCh. 3 - Prob. 38CRCh. 3 - Prob. 40CRCh. 3 - Prob. 41CRCh. 3 - Prob. 42CRCh. 3 - Prob. 43CRCh. 3 - Prob. 44CRCh. 3 - Prob. 45CRCh. 3 - Prob. 46CRCh. 3 - Prob. 47CRCh. 3 - Prob. 48CRCh. 3 - Prob. 49CRCh. 3 - Prob. 50CRCh. 3 - Prob. 51CRCh. 3 - Prob. 53CRCh. 3 - Prob. 54CRCh. 3 - Prob. 55CRCh. 3 - Prob. 56CRCh. 3 - Prob. 57CRCh. 3 - Prob. 58CRCh. 3 - Prob. 59CRCh. 3 - Prob. 60CRCh. 3 - Prob. 61CR
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- 4. Suppose the following functions are a general solution of: y(4) + a3y" +a2y" + a1y' + a0y = 0arrow_forward20. 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 repeatedarrow_forward4. Give a characteristic that the two functions f(x) = x and g(x) = 2* have in common.arrow_forward
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