I don’t get this question so can someone please help.!
1 answer:
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The correct answer is C.
The limit in A does exist:
The limit in B also exists: for any ,
But this alone does not prove the 2D limit exists. only captures all the paths through the origin that are straight lines.
The limit in C also exists, but it's not the same as either of the limits along the paths used in A and B.
That this value is non-zero tells us the original limit does not exist.
The claim in D is generally not correct. That is undefined does not automatically mean the limit doesn't exist. A simpler example:
yet is undefined.