Multivariable Calculus
Module – 3
Lecture Class-2
(Continuity)
By
Dr Hemant Kumar Nashine
Department of Mathematics, SAS,
VIT Vellore
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X-axis
Function of two variables
Y-axis
Z-axis

Continuity for Functions of Two
Variables
27-Aug-19
Dr Hemant K Nashine, Professor
2

Some facts about
continuous functions:
Algebraic combinations of continuous functions
are continuous at every point at which all the
functions involved are defined.
This
means
that
sums,
differences,
constant
multiples,
products,
quotients,
and
powers
of
continuous
functions
are
continuous
where
defined.
In particular, polynomials and rational functions of
two variables are continuous at every point at
which they are defined.
27-Aug-19
Dr Hemant K Nashine, Professor
3