help my son to answer the question

[Skywalker334]

 

[tkhunny]

If your son is studying multi-variable calculus, are you sure he can't ask his own questions?

The problem with the jump to multiple variables is the number of approaches. When it was y = f(x), one can approach only from the positive side of the x-axis or the negative side of the x-axis. With multiple variables, there is no such convenience. One must first pick a path.

Along the x-axis? Set y = 0, if it is possible, and explore the limit.
Along the y-axis? Set x = 0, if it is possible, and explore the limit.
Along the line x = y? Set x = y, if it is possible, and explore the limit?
etc.

Same idea applies here as with y = f(x), that is, if you find two limits that don't match up, you're done. NOT like y = f(x), If you find 3 million limits that do match up, you're still not done. ALL directions must be the same. Again, in a single variable, there were only two. Now, there are infinitely many that must agree. You must examine the situation for qualitative differences.

Now, let's see your work.

 

[Skywalker334]

Much obliged! I want to help his homework as a father you know ı feel useless

 

[tkhunny]

Much obliged! I want to help his homework as a father you know ı feel useless

My children almost never wanted my help. Apparently, I was too mean. Oh, well...

As a general rule, we want to see your work on the question. We can deliver lectures, sure, but you will get more out of it if we can talk more specific nitty-gritty. Frankly, you probably already consumed the course material, anyway. Will another lecture do you any good? Maybe...

 

[Steven G]

This problem is exactly the same problem which ironman23 posted 4 different times and showed no work each time.

I think the admins can see if this post came from the same ip address as the other posts. If so then this person really needs to be banned.

Of course if this is really a different person then welcome to the forum.