Find the limit.
So I said, let
If then
.....does approach from the right of left?
Sorry, i'm a bit rusty on limits. I haven't seen them in a while! Thanks for the help.
Hello,
It's ok for the beginning
There's just a problem for the limit of t.
When x tends to 7-, this means that x tends to 7, and x is <7.
So t=7-x indeed tends to 0, but is t<0 or >0 ?
--------> x<7 --> -x>-7 ---> 7-x>0
Therefore, t tends to 0, with t>0, which is written " "
Is it clear for you ?
To expand upon Moo's explanation
Means as you put a number an ifinitisemally bit smaller than 7 in you get out an infinitesimally small positive number
and a constant divided by an infinitesmially small positive number is ∞...So therefore
this is limit is not formally but informally equivalent to
Ok this is a good time to ask a serious question. This in no way despite if it does is a sarcastic or mean-spirited question?
Ok on here I use non-mathematically correct terms to help explain concepts to people....should I not do that and have them possibly get bogged down in mathematical language or should I say this is a good way of conceptualizing it with the caveat that it is technically incorrect as I did above?
I don't understand your question
As far as I know, "infinitesimal" is a mathematical term, and Newton and Leibniz indeed have to do with this concept...Ok on here I use non-mathematically correct terms to help explain concepts to people....
Well, explaining to someone that if "a constant is divided by an infinitesimal thing, it is ∞".should I not do that and have them possibly get bogged down in mathematical language or should I say this is a good way of conceptualizing it with the caveat that it is technically incorrect as I did above?
∞ is just a writing convention, it's not a number.
You didn't even mention "infinity".
Not that I'm able to explain, but I try not to get into concepts I don't really master...
However, if I had to explain... :
is positive, because we showed that t > 0, and so is 3.
When you divide by a very very small number, it's like counting how many times you have this small number in the upper number (3). For example, there are 10 times 0.1 in 1. If we decrease 0.1 into 0.01, there will be 100 of these.
Here, t becomes very small, so small that there would be a very large number of them in 3...
This is the infinity...
(this latter part has nothing to do with a real explanation... i'm just trying to clarify out what has been said before)
The original question asked about a limit as x approached 7 from below. This is indicative of a non-informal approach to limits. As such use of infinitesimals are to be deprecated as an explanatory aid.
Also Bishop Berkeley's criticisms of the use of infinitesimals are relevant.
RonL