MATHEMATICS  THEORY



Function 
The quantity relationship of
function y = x^{2} + x + 1


If the quantity of y is determined
by another value x, then y is a function of x. If f denotes the
function, then the formula y = f(x) indicate y depends on x. Thus y is
a dependent variable and x is a independent variable. An
example
of a function would be:
y = x^{2} + x + 1
The diagram on the left shows that the quantity of y which is equal to
x^{2} + x + 1
depends on the value of x.




Limit of a Function



If for each positive ε, no
matter how small, there is a corresponding positive δ such
that if
then
In this situation, the limit of f(x) is A as x approaches
a, and it can be written as:






Limits Involving Infinity

In this segment, three kind of situations will be discussed. 



The limit of f(x) is infinity
when x approaches 1 

 The limit of f(x) is ∞ as x approaches a if for each number B, no matter how large, there is a corresponding positive δ, such that if
then
f(x) > B
Its notation is




The limit of f(x) is 1
when x approaches +∞ 

 The limit of f(x) is A as x approaches ∞ if
for each positive ε, no matter how small,
there is a corresponding B such that if
x > B
then
Its notation is




The limit of f(x) is ∞ when x
approaches
∞ 

 The limit of f(x) is ∞ as x approaches ∞ if for each number B, no matter how large, there is a corresponding C, such that if
x< C
then
f(x) < B
Its notation is




Summary


Summary


This section introduces limit of a function and three cases involving infinity. When discussing limit of a function, it must be the limit of a specific point. 


