Do we rely on certain intuition or is there an unofficial general crude checklist I should follow?
I had a friend telling me that if the sum of the powers on the numerator is smaller then the denominator, there is a higher chance that it may not exists.
And if the sum of powers on the numerator is higher then the denominator, most likely, it exists.
Also if there is a sin or cos or e-constant, it most likely exists.
How can I know what to do at the first glance given so little time exists for me in exam to ponder? If I spend all my time on figuring out a two-path test when the limit exists, that would be a huge disaster.
Is this one of those cases where practice makes perfect?
Please give me a hint and where do you get the hint.
I need a hint for this too.
Common methods I have learnt for reference: Two-Path test, Polar Coordinates, Spherical Coordinates, Mean Value Theorem using inequalities.