SOTUIONS Ii part (a).] ane for which plution whose 32. (a) Show that a solution from the family in part (a) of Problem 31 that satisfies y' = y², y(1) = 1, is y = 1/(2 – x). (b) Then show that a solution from the family in part (a) of Problem 31 that satisfies y' = y², y(3) = –1, is y = 1/(2 – x). (c) Are the solutions in parts (a) and (b) the same? 33. (a) Verify that 3x² – y² = c is a one-parameter family of solutions of the differential equation y dy/dx = 3x. (b) By hand, sketch the graph of the implicit solution 3x – y = 3. Find all explicit solutions y = 4(x) of the in part (a) defined by this relation. Give the interval I of definition of each explicit solution. uarantees that nique solution (c) The point (-2, 3) is on the graph of 3x2 – y² = 3, but which of the explicit solutions in part (b) satisfies y(-2) = 3? solutions of 34. (a) Use the family of solutions in part (a) of Problem 33 to ch member roblem find an implicit solution of the initial-value problem ydy/dx = 3x, y(2) = -4. Then, by hand, sketch the graph of the explicit solution of this problem and give its he xy-plane uld have a interval I of definition. = 3x that pass (b) Are there any explicit solutions of y dy/dx through the origin? In Problems 35–38 the graph of a member of a family of solutions of a second-order differential equation dy/dx2 = f(x, y, y') is given. Match the solution curve with at least one pair of the following initial conditions. ether this (a) y(1) = 1, y'(1) = -2 problem in (b) y(-1) = 0, y'(-1) = -4 family of y?. (c) y(1) = 1, y'(1) = 2 (d) y(0) = -1, y'(0) = 2 tinuous ev- (e) y(0) = -1, y'(0) = 0 e taken to ons in part · initial-value o = 0 is in is not defined (f) y(0) = -4, y'(0) = -2 35. pr the solution family of х ous every- aken to be amily in ution from FIGURE 1.2.7 Graph for Problem 35 Determine Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-202
SOTUIONS Ii part (a).] ane for which plution whose 32. (a) Show that a solution from the family in part (a) of Problem 31 that satisfies y' = y², y(1) = 1, is y = 1/(2 – x). (b) Then show that a solution from the family in part (a) of Problem 31 that satisfies y' = y², y(3) = –1, is y = 1/(2 – x). (c) Are the solutions in parts (a) and (b) the same? 33. (a) Verify that 3x² – y² = c is a one-parameter family of solutions of the differential equation y dy/dx = 3x. (b) By hand, sketch the graph of the implicit solution 3x – y = 3. Find all explicit solutions y = 4(x) of the in part (a) defined by this relation. Give the interval I of definition of each explicit solution. uarantees that nique solution (c) The point (-2, 3) is on the graph of 3x2 – y² = 3, but which of the explicit solutions in part (b) satisfies y(-2) = 3? solutions of 34. (a) Use the family of solutions in part (a) of Problem 33 to ch member roblem find an implicit solution of the initial-value problem ydy/dx = 3x, y(2) = -4. Then, by hand, sketch the graph of the explicit solution of this problem and give its he xy-plane uld have a interval I of definition. = 3x that pass (b) Are there any explicit solutions of y dy/dx through the origin? In Problems 35–38 the graph of a member of a family of solutions of a second-order differential equation dy/dx2 = f(x, y, y') is given. Match the solution curve with at least one pair of the following initial conditions. ether this (a) y(1) = 1, y'(1) = -2 problem in (b) y(-1) = 0, y'(-1) = -4 family of y?. (c) y(1) = 1, y'(1) = 2 (d) y(0) = -1, y'(0) = 2 tinuous ev- (e) y(0) = -1, y'(0) = 0 e taken to ons in part · initial-value o = 0 is in is not defined (f) y(0) = -4, y'(0) = -2 35. pr the solution family of х ous every- aken to be amily in ution from FIGURE 1.2.7 Graph for Problem 35 Determine Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-202
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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Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
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#35 please
![SOTUIONS Ii
part (a).]
ane for which
plution whose
32. (a) Show that a solution from the family in part (a) of Problem 31
that satisfies y' = y², y(1) = 1, is y = 1/(2 – x).
(b) Then show that a solution from the family in part (a)
of Problem 31 that satisfies y' = y², y(3) = –1, is
y = 1/(2 – x).
(c) Are the solutions in parts (a) and (b) the same?
33. (a) Verify that 3x² – y² = c is a one-parameter family of
solutions of the differential equation y dy/dx = 3x.
(b) By hand, sketch the graph of the implicit solution
3x – y = 3. Find all explicit solutions y = 4(x) of the
in part (a) defined by this relation. Give the interval I
of definition of each explicit solution.
uarantees that
nique solution
(c) The point (-2, 3) is on the graph of 3x2 – y² = 3,
but which of the explicit solutions in part (b) satisfies
y(-2) = 3?
solutions of
34. (a) Use the family of solutions in part (a) of Problem 33 to
ch member
roblem
find an implicit solution of the initial-value problem
ydy/dx = 3x, y(2) = -4. Then, by hand, sketch the
graph of the explicit solution of this problem and give its
he xy-plane
uld have a
interval I of definition.
= 3x that pass
(b) Are there any explicit solutions of y dy/dx
through the origin?
In Problems 35–38 the graph of a member of a family of solutions
of a second-order differential equation dy/dx2 = f(x, y, y') is given.
Match the solution curve with at least one pair of the following initial
conditions.
ether this
(a) y(1) = 1, y'(1) = -2
problem in
(b) y(-1) = 0, y'(-1) = -4
family of
y?.
(c) y(1) = 1, y'(1) = 2
(d) y(0) = -1, y'(0) = 2
tinuous ev-
(e) y(0) = -1, y'(0) = 0
e taken to
ons in part
· initial-value
o = 0 is in
is not defined
(f) y(0) = -4, y'(0) = -2
35.
pr the solution
family of
х
ous every-
aken to be
amily in
ution from
FIGURE 1.2.7 Graph for Problem 35
Determine
Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-202](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc074fc7e-4e48-46f1-bfc4-aee6ba4e6262%2Fe2430908-eae9-4a0d-b759-5f4a2de97921%2F9ha3g2p.png&w=3840&q=75)
Transcribed Image Text:SOTUIONS Ii
part (a).]
ane for which
plution whose
32. (a) Show that a solution from the family in part (a) of Problem 31
that satisfies y' = y², y(1) = 1, is y = 1/(2 – x).
(b) Then show that a solution from the family in part (a)
of Problem 31 that satisfies y' = y², y(3) = –1, is
y = 1/(2 – x).
(c) Are the solutions in parts (a) and (b) the same?
33. (a) Verify that 3x² – y² = c is a one-parameter family of
solutions of the differential equation y dy/dx = 3x.
(b) By hand, sketch the graph of the implicit solution
3x – y = 3. Find all explicit solutions y = 4(x) of the
in part (a) defined by this relation. Give the interval I
of definition of each explicit solution.
uarantees that
nique solution
(c) The point (-2, 3) is on the graph of 3x2 – y² = 3,
but which of the explicit solutions in part (b) satisfies
y(-2) = 3?
solutions of
34. (a) Use the family of solutions in part (a) of Problem 33 to
ch member
roblem
find an implicit solution of the initial-value problem
ydy/dx = 3x, y(2) = -4. Then, by hand, sketch the
graph of the explicit solution of this problem and give its
he xy-plane
uld have a
interval I of definition.
= 3x that pass
(b) Are there any explicit solutions of y dy/dx
through the origin?
In Problems 35–38 the graph of a member of a family of solutions
of a second-order differential equation dy/dx2 = f(x, y, y') is given.
Match the solution curve with at least one pair of the following initial
conditions.
ether this
(a) y(1) = 1, y'(1) = -2
problem in
(b) y(-1) = 0, y'(-1) = -4
family of
y?.
(c) y(1) = 1, y'(1) = 2
(d) y(0) = -1, y'(0) = 2
tinuous ev-
(e) y(0) = -1, y'(0) = 0
e taken to
ons in part
· initial-value
o = 0 is in
is not defined
(f) y(0) = -4, y'(0) = -2
35.
pr the solution
family of
х
ous every-
aken to be
amily in
ution from
FIGURE 1.2.7 Graph for Problem 35
Determine
Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-202
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