Open study

is now brainly

With Brainly you can:

  • Get homework help from millions of students and moderators
  • Learn how to solve problems with step-by-step explanations
  • Share your knowledge and earn points by helping other students
  • Learn anywhere, anytime with the Brainly app!

A community for students.

Basic question: In the 2nd lecture on the use of limits for proving continuity of differentiable functions, is lim { [f(x) - f(x0)]/[x-x0] } = 1/[x-x0] lim [f(x) - f(x0)] if we see lim as an operator?

MIT 18.01 Single Variable Calculus (OCW)
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

\[\lim_{x \rightarrow x_{0}} \left( \frac{ f(x)-f(x_{0}) }{ x-x_{0} } \right) = \frac{1}{x-x_{0}} \lim_{x \rightarrow x_{0}} \left( f(x)-f(x_{0}) \right)\] 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.
no you can not consider it as an operator. however, it is more beneficial to [/delta x/] instead of \[x-x_0\]
x -> x0, then f(x) - f(x0) is changing but also x - x0 is changing therefore you cannot treat x-x0 as constant and put it before limit

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

Not the answer you are looking for?

Search for more explanations.

Ask your own question