Learning Materials
Features
Discover
Chapter 1: Q8-3-14P (page 1)
Using (3.9), find the general solution of each of the following differential equations. Compare a computer solution and, if necessary, reconcile it with yours. Hint: See comments just after()3.9, and Example 1.
14.
Hint: For Problems 12to 14, solve forx in terms of y.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Solve for all possible values of the real numbersand in the following equations.
(a) Using computer or tables (or see Chapter Section ),verify that,and also verify that the error in approximating the sum of the series by the first five terms is approximately .
(b) By computer or tables verify that
the sum of the first five terms is
(c) Prove theorem . Hint: The error is .
Use the fact that the absolute value of a sum is less than or equal to the sum of the absolute values. Then use the fact that to replace all by , and write the appropriate inequality. Sum the geometric series to get the result.
Evaluate the following indeterminate forms by using L’Hopital’s rule and check your results by computer. (Note that Maclaurin series would not be useful here because xdoes not tend to zero, or because a function (In x, for example) is not expandable in a Maclaurin series.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Exams 
GCSE 
IGCSE 
AS 
A Level 
International A Level 
University Admissions Tests 
Flashcards 
Vaia AI 
Notes 
Study Plans 
Study Sets 
Find a job 
Find a degree 
Student Deals 
Magazine 
Mobile App