What are Limits?Please explain Limits in absolutely simple langusge without the usage of any technical language. Actually, i am a newbie to...

There are different kinds of limits in calculus --the
limit as x approaches c of a function, the limit of a sequence or series, etc... In a
typical first semester calculus class you are probably working with
`lim_(x->c)f(x)` .

There area large number of
technical things to consider, but basically what `lim_(x->c)f(x)=L` says is that
as x gets arbitrarily close to c, f(x) gets arbitrarily close to L. (The rub comes when
we try to define "arbitrarily close"-- for that we use a `delta-epsi`
definition).

If you look at a table of values for f(x),
when x is close to c the function value (y=f(x) ) is close to L. The closer x gets to c,
in general the closer y gets to L.

If you graph f(x), as
you trace along the curve and get closer to c in the x-direction, the y-value is getting
closer to L.

You might consider when a function fails to
have a limit at a point -- here are some possibilities:

(1)
If the function grows without bound as x nears c (e.g. `y=1/x` with c=0) then there is
no limit since as x approaches c the y-value does not approach a number L-- it just
keeps growing past any number you specify.

(2) If the
function experiences a "jump" at c: define f(x) to be x if x>0, and f(x) to be
-2x-3 for `x<=0` , and let c=0. As you approach c from the left, f(x) approaches
-3; but as you approach 0 from the right, f(x) approaches 0. Note that as x approaches
0, f(x) does not approach a number L; it approaches two different numbers so there is no
limit.

(3) Finally, consider a function with infinite
oscillations at c. Since the function goes from its maximum to its minimum an infinite
number of times, you cannot say that f(x) approaches any single
number.