 
 
Students you can to the playlist and watch my videos
as here my complete playlist is arranged topic wise
so you won't face any problem
as many students complain that we are not getting this topic that topic
so here the playlist is arranged topic wise
so you can go and watch all my videos here
Hello students myself Dr. Gajendra Purohit and you are watching my youtube
channel where I upload videos for
higher mathematics, bsc and engineering students. Students if you are
preparing for CSIR-NET, GATE, IIT-JEM and IAS
so in that also my videos are very helpful for you. Students
here you can go to the playlist and watch my videos
and students the topic that I have taken here is
limit continuity and differentiability for the function of two variable. In this
series I have taken two videos for limit
in which for the first video I have made you do questions on epsilon delta definition
and in second I have made you do the questions on limit
where the limit of the function does not exists. So these types of questions I have made you do
which includes the questions on independent path
so you can go to the I icon
and watch my old videos
a if you will see those videos you will understand this much easily
so students see continuity of function of two variable
students as we study continuity of function in one variable
in 12th class. This is also the same concept
as in 12th class the concept is that the limit should exist
and it's value should be equal to the function which means that
point at the value
should be equal to the value of the function .Right? so the same
definition is here also
but there will be two variables that is x and y
so then let f (xy) be the continuous  function of two variable
defined in open region D of R2
 
 
 
so that this point the function should be defined
 
 
 
 
 
 
so if this happens the function is continuous. See between limit and continuity there is only one
difference. What happens in limit is that
we directly calculate the limit and check
that if it exists it is good
but what happen in continuity is that
limit should exists but the point where we are checking that point
if we keep it equal to the function it should come equal to the limit and if this happens
then the function is
continuous. Now I will explain you this with an example
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
so here this will not be continuous as here the value of limit is not equal to the value of the function
so let's take more
example and then we will move forward
so students see here the question
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
we will take one more example and then finish this
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
let's see one more example and then finish this
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
if the value of m becomes 1 then also it's value will come to be 0 which means that
it's limit will be
exist what so ever path we take. Right? as y=x
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
so this is how we solve the question. So students I feel
that you must have understood the question
and students be with me
these types of questions I am bringing for you and even more good
questions I will bring for you and these types of questions in CSIR-NET
GATE type of exams are asked and even in IIT-JEM
these types of questions
can come and more related concepts to this I will bring for you
and now in my next video I will discuss differentiability
and function of two variable and how we check the differentiability there
so students be with me and I will upload good content for you
and if my content
is liked by you then please do comment
and do like , share
with your friends and we with me and you can go to these videos and
watch my playlist
and you can go here and subscribe to my channel. Thank you so much. Bye
