In Exercises 45-46, we demonstrate that, in general, you antiderivative of a product of functions by taking a prod tives of each. 45. Show that G(x) = x²e* is not an antiderivative of H(x) = 2xe* - 2e* is. 46. Show that G(x) = 3x² sinx is not an antideriv 6x cos x but H(x) = 6x sin x + 6 cos x is. In Exercises 47-60, solve the initial value problem. dy dx 47) 49. 50. 51. (53. 54. ale ale ale ale ale dy dt dy dx dy dt dx = x³, y(0) = 4 dy (6.0) 001 to ovi = 2t +9t², y(1) = 2 dy 48. 184,80 dt = 8x³ + 3x², y(2) = 0 = √t, y(1) = 1 (0)1-(0) 52. 0015 = (4t+3)-2, y(1) = 0 dz dy = (3x+2)³, y(0)=1, ai sgasto isto goini art of his to bong - dt = 3 = t
In Exercises 45-46, we demonstrate that, in general, you antiderivative of a product of functions by taking a prod tives of each. 45. Show that G(x) = x²e* is not an antiderivative of H(x) = 2xe* - 2e* is. 46. Show that G(x) = 3x² sinx is not an antideriv 6x cos x but H(x) = 6x sin x + 6 cos x is. In Exercises 47-60, solve the initial value problem. dy dx 47) 49. 50. 51. (53. 54. ale ale ale ale ale dy dt dy dx dy dt dx = x³, y(0) = 4 dy (6.0) 001 to ovi = 2t +9t², y(1) = 2 dy 48. 184,80 dt = 8x³ + 3x², y(2) = 0 = √t, y(1) = 1 (0)1-(0) 52. 0015 = (4t+3)-2, y(1) = 0 dz dy = (3x+2)³, y(0)=1, ai sgasto isto goini art of his to bong - dt = 3 = t
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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How do you solve the initial value for problem 53?
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Transcribed Image Text:antiderivative
tives of each.
In Exercises 45-46, we demonstrate that, in general, you
of a product of functions by taking a prod
45. Show that G(x) = x²ex is not an antiderivative of
H(x) = 2xe* - 2et is.
46. Show that G(x) = 3x² sinx is not an antideriv
6x cos x but H(x) = 6x sin x + 6 cos x is.
In Exercises 47-60, solve the initial value problem.
dy
dx
47.
49.
50.
51.
(53.
54.
(55.
56.
a ala ale ale ale ale
dy
dt
dy
dx
dy
dt
dy
dx
dy
dt
dy
dx
dy
dx
= x³, y(0) = 4
nodi..
= 2t +9t², y(1) = 2
= √t, y(1) = 1
= 8x³ + 3x², y(2) = 0
-
(3x + 2)³, y(0) = 1 azi
ONDE
:sin x, y (7)
not to
= (4t+3)-2, y(1) = 0
sec² x, y
dy
48.
1789,30 dt
=
(7) =
= 2
52.
dz
dt
= = 3
191
teag Be
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