University Mathematics Handbook (2015)
IX. Vector Analysis
Chapter 2. Limits and Continuity of Vector Functions
a. Constant vector 
is the limit of vector function 
when 
if for every 
there exists 
such that for every 
holding 
there holds 
. Written 
.
b. 
if and only if 
, 
, 
.
c. The limit of the sum of two vector functions is equal to the sum of their limits.
d. The limit of an inner (cross) product of two vector functions is equal to the inner (cross) product of their limits.
e. Function 
is continuous at point 
if it is defined in the neighborhood of , and 
.
f. The sum, inner product and cross product of continuous vector functions is a continuous vector function.