The Limit, as x approaches c, of a function
f(x), is said to be equal to L if the value of f(x) gets "closer and
closer" to L as x gets "closer and closer" to c. This page
presents a mathematically rigorous explanation of this, and also introduces some
special uses of limits.
The Derivative is a special limit -- the
derivative of f(x) with respect to x (written d/dx f(x)) is
lim_{h−>0} (f(x+h)-f(x))/h. This page explains the significance
of this special limit.
The Integral is another special limit, and
you can also think of it as an "anti-derivative" plus a
constant. This page introduces these concepts.
First
Year Calculus
by
WIlliam Chen,
an excellent roundup of all a student needs to know in his first year of
calculus, including the number system, number system, functions, limits,
continuity, differentiation, exponential function, definite integral and its
applications, integration techniques.