Limits (Mathamatics)19 Aug 2014
[Warning: These are more like my notes which I make public so that if at all there are some stupid people like me, these would come handy]
A limit is the value that a function or sequence “approaches” as the input or index approaches some value.
Limit of function
This says that L is the value of function ƒ(x) when x reaches to value c.
|There is one more definition which is kind of logical evidence to this is L is the limit of function ƒ(x) with ε as a small positive real number then value of ƒ(x) lies in (L-ε,L+ε) or||ƒ(x) – L||< ε|
I found this amazing question
Adding the most upvoted example here
The reading of your speedometer (e.g., 85 km/h) is a limit in the real world. Maybe you think speed is speed, why not 85 km/h. But in fact your speed is changing continuously during time, and the only “solid”, i.e., “limitless” data you have is that it took you exactly 2 hours to drive the 150 km from A to B. The figure your speedometer gives you is at each instant t0 of your travel the limit
where s(t) denotes the distance travelled up to time t.
And the most simple to understand (for me)
If I keep tossing a coin as long as it takes, how likely am I to never toss a head?
Possibility of getting a head is (1/2) if I toss the coin once.
Now if I toss N times P(N) = (1/2)^N
Now this probability would be zero if N is ∞.
Mathematical representation of the question is
P(N) = (1/2)^N find N for which P(N) = 0
and Answer to the given question is