Main Area and Open Discussion > Living Room

Math is an Attitude

<< < (3/3)

tsaint:
I'm a bit worried about the limit(x-8)^-1 as x->8 being equal to infinity. I'd think the limit doesn't exist.
-tsaint (August 01, 2006, 03:17 AM)
--- End quote ---

I believe that while (x-8)^1 for x = 8 doesn't exist, the limit as x tends towards 8 does, and that limit is infinity.
-Eóin (August 10, 2006, 04:15 PM)
--- End quote ---
I was led to believe that a limit only existed pv the left limit equalled the right limit, which isn't the case here. This case is completely unlike eg lim x->2 (x-4)/(x^2-4x) where there's a discontinuity at x=2 but the lim equals 1/2

Eóin:
I was led to believe that a limit only existed pv the left limit equalled the right limit, which isn't the case here.-tsaint (August 10, 2006, 05:30 PM)
--- End quote ---

Ah yes, excellent point and I stand corrected. I suppose you could add "x belongs to [0,8)" and then perhaps it'd be ok but thats moving the goal posts :) .

Carol Haynes:
I'm a bit worried about the limit(x-8)^-1 as x->8 being equal to infinity. I'd think the limit doesn't exist.
Think I like the student answer better than the teacher example-tsaint (August 01, 2006, 03:17 AM)
--- End quote ---

Actually I agree with you ... infinity isn't a limit. If there are limits for y=1/(x-8) they are x=8 because x can never actually equal 8 but can approach as close as you like and y=0 as y can never equal 0. Here is a quick and dirty graph ...



Technically x=8 and y=0 are called discontinuities - not limits.

A limit is like somone walking towards a fixed point but each step covers half the distance - they will never reach their target but the target is the limit !

housetier:
Someone posted a lot of math jokes at the Durham University Mathematical Society. They are not all very funny, but some I liked for obscure reasons. 
(...)I'll do algebra, I'll do trig, and I'll even do statistics, but graphing is where I draw the line!
--- End quote ---

I am sure you have your favorites too :)

Eóin:
Some of those are quite good. On the subject of Math jokes, here is a collection I compiled a while back.

Navigation

[0] Message Index

[*] Previous page