Doubt from limits

Why is the solution in 2nd image wrong??

You cant subtract infinity from infinity. Its undefined

Then in the same way we can’t cancel x terms in questions where we take some power of x common… Because that is always infinity / infinity form right??

I dont get the point. We dont cancel infinity by infinity too

Sorry… Not exactly cancel… But we divide x^2 or something in those questions where we use expansions of sinx, tanx etc…
So how can we divide by infinity?

It is something like this in the book…
And this type of problems as in given as an example below it…

And i have one more doubt…
How do i know whether to use sandwich theorem or the method in which we convert a summation to integral…??

Dont know bro. We seemingly cancel it algebraically.

Practice 4-5 questions of sandwich theorem and you will realise it yourself

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Ohk… Can you ask your sir?

Okay… Thank you

practice a lot of questions bro after a certain period you’ll just know which method to do just by scanning the question

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Ok bro… Thanks…