A community for students.
Here's the question you clicked on:
 0 viewing
LaundryDog
 2 years ago
Basic question: In the 2nd lecture on the use of limits for proving continuity of differentiable functions, is lim { [f(x)  f(x0)]/[xx0] } = 1/[xx0] lim [f(x)  f(x0)] if we see lim as an operator?
LaundryDog
 2 years ago
Basic question: In the 2nd lecture on the use of limits for proving continuity of differentiable functions, is lim { [f(x)  f(x0)]/[xx0] } = 1/[xx0] lim [f(x)  f(x0)] if we see lim as an operator?

This Question is Open

Waynex
 2 years ago
Best ResponseYou've already chosen the best response.2\[\lim_{x \rightarrow x_{0}} \left( \frac{ f(x)f(x_{0}) }{ xx_{0} } \right) = \frac{1}{xx_{0}} \lim_{x \rightarrow x_{0}} \left( f(x)f(x_{0}) \right)\] If you are asking if the right hand side represents a valid algebraic manipulation of the left hand side, the answer is no. In the denominator, x is not a constant; therefore, it cannot be moved out of the limit.

hemn
 2 years ago
Best ResponseYou've already chosen the best response.0no you can not consider it as an operator. however, it is more beneficial to [/delta x/] instead of \[xx_0\]

fantastic001
 2 years ago
Best ResponseYou've already chosen the best response.0x > x0, then f(x)  f(x0) is changing but also x  x0 is changing therefore you cannot treat xx0 as constant and put it before limit
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.