Lecture
Let function defined around the number
(at
function ƒ may not be defined). The number A is called the limit of the function.
with x tending to
(
), if for any arbitrarily small number ε > 0 there exists a number δ > 0 such that for all x satisfying the condition
inequality holds
.
Expression means the limit function
with x tending to
is equal to a.
If for any arbitrarily large positive number M there is a number δ > 0 such that for all x satisfying the condition inequality holds
then say function
is infinitely large when x tends to
and write down:
.
If this value , then write:
, what if
, then write:
. If a
then function
is called an infinitely small value when x tends to
.
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Mathematical analysis. Differential calculus
Terms: Mathematical analysis. Differential calculus