Show that is continuous at and both the partial derivatives of exist but are not bounded in for any .
Show that both and exist at every but is not continuous at .
Show that none of the partial derivatives of exist at although is continuous at .
Let , and be such that both and exist and are bounded in
(Such a function is said to be homogeneous of degree .) If the first order partial derivatives of exist and are continuous, then show that
is continuous at 
and both the partial derivatives of 
exist but 
for any 
. 
be defined by 
and 
exist at every 
but 
is not continuous at 
. 
and
exist at 
although 
is continuous at 
. 
, 
and 
be such that both 
and 
exist and are bounded in
for some 
. Prove that 
is continuous at 
.
has the property that there exists 
such that 
.) If the first order partial derivatives of 
exist and are continuous, then show that 
