Question

Check whether f(x)=1/x is continuous or not ?

Answer 1

What happens if x=0?

Answer 2

There is an asymptote (vertical)

Answer 3

For a function to be continuous, http://www.cliffsnotes.com/study_guide/Continuity.topicArticleId-39909,articleId-39876.html

Does f(0) exist, for f(x)=1/x?

Answer 4

so lim x->0 does not exist bcoz LHL = -infinity and RHL = infinity ?

Answer 5

That too, but is the first condition even met? Does f(0) exist?

Answer 6

If f(0) = infinity, can we say f(0) exists ? :P

Answer 7

haha, we can not :P

So f(0) does not exist, and the limits at the left and right are not equal (and they also do not equal f(0), because... it doesn't exist!)

Answer 8

Okayy! Dumb me

Answer 9

You can't really even say f(0) = infinity even in terms of the limits (f(0) is just undefined), since it approaches -inf from the left, and +inf from the right, compared to something like 1/x^2, which approaches +inf from both the left and right (1/x^2 is still undefined for x=0, since a function can't actually be equal to infinity... it can just approach it)

Answer 10

ouch.. Thanks you rock

Answer 11

You can also plot it on google: https://www.google.com/search?q=1%2Fx&aq=f&oq=1%2Fx&aqs=chrome.0.59l2j58j5j0j62.2465j0&sourceid=chrome&ie=UTF-8