Smooth functions
Not what you're looking for?
PLEASE see attachment for proper display of equations.
Let f be a function from N to R+ . Function f is eventually nondecreasing if
such that . Function f is smooth if it is eventually
nondecreasing and such that .
(a) Is the function + such that a smooth function? Verify!
(b) Is the function + such that = a smooth function? Verify!
Purchase this Solution
Solution Summary
Smooth functions are analyzed. Increasing and nondecreasing functions are provided.
Solution Preview
a.)
because,
f(n) = n*log(n), n belong to N.
for m,n belong to N and m <= n:
f(m) = m*lg(m)
and,
f(n) = n*lg(n)
because, lg(n) is slow increasing function, therefore,
f(n) >= f(m)
=> f(n) is non-decreasing function Ok.
Now,
for k,n belong to N and ...
Education
- BEng, Allahabad University, India
- MSc , Pune University, India
- PhD (IP), Pune University, India
Recent Feedback
- " In question 2, you incorrectly add in the $3.00 dividend that was just paid to determine the value of the stock price using the dividend discount model. In question 4 response, it should have also been recognized that dividend discount models are not useful if any of the parameters used in the model are inaccurate. "
- "feedback: fail to recognize the operating cash flow will not begin until the end of year 3."
- "Answer was correct"
- "Great thanks"
- "Perfect solution..thank you"
Purchase this Solution
Free BrainMass Quizzes
Inserting and deleting in a linked list
This quiz tests your understanding of how to insert and delete elements in a linked list. Understanding of the use of linked lists, and the related performance aspects, is an important fundamental skill of computer science data structures.
Basic UNIX commands
Use this quiz to check your knowledge of a few common UNIX commands. The quiz covers some of the most essential UNIX commands and their basic usage. If you can pass this quiz then you are clearly on your way to becoming an effective UNIX command line user.
Javscript Basics
Quiz on basics of javascript programming language.
Word 2010: Tables
Have you never worked with Tables in Word 2010? Maybe it has been a while since you have used a Table in Word and you need to brush up on your skills. Several keywords and popular options are discussed as you go through this quiz.
C# variables and classes
This quiz contains questions about C# classes and variables.