![Fundamentals of Differential Equations and Boundary Value Problems](https://www.bartleby.com/isbn_cover_images/9780321977106/9780321977106_largeCoverImage.gif)
Concept explainers
Initial value theorem. Apply the relation
to argue that for any function
![Check Mark](/static/check-mark.png)
Want to see the full answer?
Check out a sample textbook solution![Blurred answer](/static/blurred-answer.jpg)
Chapter 7 Solutions
Fundamentals of Differential Equations and Boundary Value Problems
- Determine whether each of the following statements is true or false, and explain why. The chain rule is used to take the derivative of a product of functions.arrow_forwardThis exercise shows another way to derive the formula for the derivative of the natural logarithm function using the definition of the derivative. a. Using the definition of the derivative, show that d(lnx)dx=limh0ln(1+hx)1h. b. Eliminate h from the result in part a using the substitution h=x/m to show that d(lnx)dx=limmln[(1+1m)m]1/x c. What property should the function g have that would yield limmg(h(m))=g(limmh(m))? Assuming that the natural logarithm has this property, and using the result about (1+1/m)m from Section 2.1, show that d(lnx)dx=lne1/x=1x.arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
![Text book image](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)