Precalculus: A Unit Circle Approach
2nd Edition
ISBN: 9780321825391
Author: Ratti
Publisher: PEARSON
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Chapter A.3, Problem 56E
In Exercises 53-66; perform the indicated operations and simplify the result. Leave the numerator and denominator in your answer in factored form.
56.
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What is a solution to a differential equation? We said that a differential equation is an equation that
describes the derivative, or derivatives, of a function that is unknown to us. By a solution to a differential
equation, we mean simply a function that satisfies this description.
2. Here is a differential equation which describes an unknown position function s(t):
ds
dt
318
4t+1,
ds
(a) To check that s(t) = 2t2 + t is a solution to this differential equation, calculate
you really do get 4t +1.
and check that
dt'
(b) Is s(t) = 2t2 +++ 4 also a solution to this differential equation?
(c) Is s(t)=2t2 + 3t also a solution to this differential equation?
ds
1
dt
(d) To find all possible solutions, start with the differential equation = 4t + 1, then move dt to the
right side of the equation by multiplying, and then integrate both sides. What do you get?
(e) Does this differential equation have a unique solution, or an infinite family of solutions?
Ministry of Higher Education &
Scientific Research
Babylon University
College of Engineering -
Al musayab
Automobile Department
Subject :Engineering Analysis
Time: 2 hour
Date:27-11-2022
کورس اول تحليلات
تعمیر )
1st month exam / 1st semester (2022-2023)/11/27
Note: Answer all questions,all questions have same degree.
Q1/: Find the following for three only.
1-
4s
C-1
(+2-3)2 (219) 3.0 (6+1)) (+3+5)
(82+28-3),2-
,3-
2-1
4-
Q2/:Determine the Laplace transform of the function t sint.
Q3/: Find the Laplace transform of
1,
0≤t<2,
-2t+1,
2≤t<3,
f(t) =
3t,
t-1,
3≤t 5,
t≥ 5
Q4: Find the Fourier series corresponding to the function
0
-5
Ministry of Higher Education &
Scientific Research
Babylon University
College of Engineering -
Al musayab
Subject :Engineering Analysis
Time: 80 min
Date:11-12-2022
Automobile Department
2nd month exam / 1" semester (2022-2023)
Note: Answer all questions,all questions have same degree.
کورس اول
شعر 3
Q1/: Use a Power series to solve the differential equation:
y" - xy = 0
Q2/:Evaluate using Cauchy's residue theorem,
sinnz²+cosz²
dz, where C is z = 3
(z-1)(z-2)
Q3/:Evaluate
dz
(z²+4)2
Where C is the circle /z-i/-2,using Cauchy's residue theorem.
Examiner: Dr. Wisam N. Hassan
Chapter A.3 Solutions
Precalculus: A Unit Circle Approach
Ch. A.3 - In exercises 10, reduce each rational expression...Ch. A.3 - Prob. 2ECh. A.3 - Prob. 3ECh. A.3 - Prob. 4ECh. A.3 - Prob. 5ECh. A.3 - Prob. 6ECh. A.3 - Prob. 7ECh. A.3 - Prob. 8ECh. A.3 - In exercises1-10, reduce each rational expression...Ch. A.3 - Prob. 10E
Ch. A.3 - Prob. 11ECh. A.3 - Prob. 12ECh. A.3 - Prob. 13ECh. A.3 - Prob. 14ECh. A.3 - Prob. 15ECh. A.3 - In Exercises 11-20, multiply or divide as...Ch. A.3 - In Exercises 11-20, multiply or divide as...Ch. A.3 - In Exercises 11-20, multiply or divide as...Ch. A.3 - In Exercises 11-20, multiply or divide as...Ch. A.3 - In Exercises 11-20, multiply or divide as...Ch. A.3 - In Exercises 21-30, add and subtract as indicated....Ch. A.3 - In Exercises 21-30, add and subtract as indicated....Ch. A.3 - In Exercises 21-30, add and subtract as indicated....Ch. A.3 - Prob. 24ECh. A.3 - In Exercises 21-30, add and subtract as indicated....Ch. A.3 - In Exercises 21-30, add and subtract as indicated....Ch. A.3 - In Exercises 21-30, add and subtract as indicated....Ch. A.3 - In Exercises 21-30, add and subtract as indicated....Ch. A.3 - In Exercises 21-30, add and subtract as indicated....Ch. A.3 - In Exercises 21-30, add and subtract as indicated....Ch. A.3 - Prob. 31ECh. A.3 - Prob. 32ECh. A.3 - Prob. 33ECh. A.3 - Prob. 34ECh. A.3 - Prob. 35ECh. A.3 - Prob. 36ECh. A.3 - Prob. 37ECh. A.3 - Prob. 38ECh. A.3 - Prob. 39ECh. A.3 - Prob. 40ECh. A.3 - Prob. 41ECh. A.3 - Prob. 42ECh. A.3 - Prob. 43ECh. A.3 - Prob. 44ECh. A.3 - Prob. 45ECh. A.3 - Prob. 46ECh. A.3 - In Exercises 37-52, perform the indicated...Ch. A.3 - Prob. 48ECh. A.3 - Prob. 49ECh. A.3 - Prob. 50ECh. A.3 - Prob. 51ECh. A.3 - Prob. 52ECh. A.3 - Prob. 53ECh. A.3 - Prob. 54ECh. A.3 - In Exercises 53-66; perform the indicated...Ch. A.3 - In Exercises 53-66; perform the indicated...Ch. A.3 - Prob. 57ECh. A.3 -
In Exercises 53-66, perform the indicated...Ch. A.3 -
In Exercises 53-66, perform the indicated...Ch. A.3 -
In Exercises 53-66, perform the indicated...Ch. A.3 -
In Exercises 53-66, perform the indicated...Ch. A.3 -
In Exercises 53-66, perform the indicated...Ch. A.3 -
In Exercises 53-66, perform the indicated...Ch. A.3 -
In Exercises 53-66, perform the indicated...Ch. A.3 -
In Exercises 53-66, perform the indicated...Ch. A.3 - Prob. 66ECh. A.3 - Prob. 67ECh. A.3 - Toy box height. The height (in feet) of an open...Ch. A.3 - Diluting a mixture. A 100-gallon mixture of citrus...Ch. A.3 - Prob. 70ECh. A.3 - Prob. 71ECh. A.3 - Prob. 72E
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- Ministry of Higher Education & Scientific Research Babylon University College of Engineering - Al musayab Subject :Engineering Analysis Time: 80 min Date:11-12-2022 Automobile Department 2nd month exam / 1" semester (2022-2023) Note: Answer all questions,all questions have same degree. کورس اول شعر 3 Q1/: Use a Power series to solve the differential equation: y" - xy = 0 Q2/:Evaluate using Cauchy's residue theorem, sinnz²+cosz² dz, where C is z = 3 (z-1)(z-2) Q3/:Evaluate dz (z²+4)2 Where C is the circle /z-i/-2,using Cauchy's residue theorem. Examiner: Dr. Wisam N. Hassanarrow_forwardWhich degenerate conic is formed when a double cone is sliced through the apex by a plane parallel to the slant edge of the cone?arrow_forward1/ Solve the following: 1 x + X + cos(3X) -75 -1 2 2 (5+1) e 5² + 5 + 1 3 L -1 1 5² (5²+1) 1 5(5-5)arrow_forward
- Please can you give detailed steps on how the solutions change from complex form to real form. Thanks.arrow_forwardExamples: Solve the following differential equation using Laplace transform (e) ty"-ty+y=0 with y(0) = 0, and y'(0) = 1arrow_forwardExamples: Solve the following differential equation using Laplace transform (a) y" +2y+y=t with y(0) = 0, and y'(0) = 1arrow_forward
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