The question doesn't seem to change because both x and y approach 0, but the real difference is the x³ on the top. Along y=0: 1st case: lim (x³/(x²+0)) = lim (x) = 0 2nd case: lim (x³/(x⁴+0)) = lim (1/x) => DNE :)
There's another textbook favorite where the limit approaches zero along every path except along y = Xsquared, where it approaches 1. How do you know which paths to check?
Have you checked out my "6 methods of evaluating the limit of a multivariable function"? The link is in the description and hopefully it answers your question.
Finally I will be here from the past
How did you write this comment 2 weeks ago?
@@mohannad_139 this video was unlisted, and it was hyperlinked from another video doing some simpler limits in polar form.
The question doesn't seem to change because both x and y approach 0, but the real difference is the x³ on the top.
Along y=0:
1st case: lim (x³/(x²+0)) = lim (x) = 0
2nd case: lim (x³/(x⁴+0)) = lim (1/x) => DNE
:)
Great video
There's another textbook favorite where the limit approaches zero along every path except along y = Xsquared, where it approaches 1. How do you know which paths to check?
What's the limit in question? If we can see the form, we may be able to judge.
I have a video on "how to show nonexistence" coming soon!
I think you haven
t listed it yet
Do you have a question like this such that the limit would equal one? That’d be cool to see.
(x²+y³)/(x²+y³)
@@xinpingdonohoe3978 Well, you did answer my question, but I was hoping for something more exciting than that.
@@xinpingdonohoe3978that one is sooo hard
Have you checked out my "6 methods of evaluating the limit of a multivariable function"? The link is in the description and hopefully it answers your question.
@@bprpcalculusbasicsI was talking about a polar limit question that would approach 1. The example you have in the video approaches 0.
Ok.. but how can I see this paths in general case
This video makes me feel like when I find a bug in a video game and it gets patches :'(
wow