Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Calculus and Beyond Homework Help
Proving that limit of 1/x as x approaches 0 does not exist
Reply to thread
Message
[QUOTE="Seydlitz, post: 4483439, member: 271790"] [h2]Homework Statement [/h2] This is the classical problem of proving that ##\lim_{x \to 0} f(x) = DNE\text{ where }f(x)=\frac{1}{x}## I know there are many solutions to this problem but I just want to do it myself with your hints from scratch. [h2]The Attempt at a Solution[/h2] If we want to prove that a limit does not exist we can show the negation of the limit definition or show that the limit from left and right are not equal. The negation of the limit definition basically boils down to the fact that there is some ##x## which satisfies ##0<|x-a|<\delta## but not ##|f(x)-l|<\epsilon##, alternatively it satisfies ##|f(x)-l|>\epsilon##. I'm a bit lost on how to find this ##x## rigorously. It seems that there are always many different methods but I still can't get the feel of it intuitively. What is clear to me is this will always be true ##0<|x|<\delta## and the function will go very large as delta is reduced. That means it doesn't satisfy the ##|f(x)-l|<\epsilon## condition and that ##|\frac{1}{x}-l|>\epsilon## But what is ##l## in this case and how to complete the proof? [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Calculus and Beyond Homework Help
Proving that limit of 1/x as x approaches 0 does not exist
Back
Top