A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
f*(a)=lim as h>0 ([f(a+h)]^2[f(a)]^2)/h We were asked to express it in terms of f'(a) =lim h>0 (f(a+h)f(a))/h
anonymous
 5 years ago
f*(a)=lim as h>0 ([f(a+h)]^2[f(a)]^2)/h We were asked to express it in terms of f'(a) =lim h>0 (f(a+h)f(a))/h

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0This is the alternate definition of a derivative. I'll take a look at it and get back to you if I figure it out. If not, you can look in your textbook under the derivative section and look for the term alternate definition of a derivative for examples. They all solve in similar ways.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok so the method to solve this is expand f(a+h)^2 and f(a)^2. The a^2 terms will go to zero. (a^2a^2 = 0) leaving you with a higher degree H term in the numerator. Cancel all h's in numerator and denominator. Any terms that still have an H term go to 0. This leaves you with the derivative. For your problem specifically: = lim h> 0 ((a^2 + 2ah + h^2)  a^2)/ (h) = lim h> 0 (2ah+h^2)/h = lim h> 0 (2a + h)/1 = (2a + 0)/1 = 2a Note that I stopped writing the lim h>0 after I plugged it in, and I plugged it in after I removed h from the denominator.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So to express this in terms of f'(a) would be 2f(a) f'(a)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I'm not sure about that notation i'm sorry. You asked for it to be expressed in terms of f'(a) and that is equal to 2a. Perhaps the question was asking you to solve the question with the definition of a derivative, rather than in terms of the equation for the definition of a derivative. And I apologize, I misinformed you. This is the regular definition of a derivative. Not the alternative definition. You'll probably cover that next. lim x>a (f(x)f(a))/(xa)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.