Looking for a textbook for Advanced Limits

[askor]

As I can't find it in my basic calculus book, can someone please tell me what book that taught a limit theory and problem like these?

Thank you

 

[fresh_42]

You can have a look into this one:
https://openstax.org/details/books/calculus-volume-1
https://en.wikipedia.org/wiki/L'Hôpital's_rule

 

[askor]

Are you sure that the openstax calculus book cover all of the limit examples I posted in post #1?

I need a calculus book that contain many, many examples of limit problem I posted in post #1.

 

[fresh_42]

Here is one: https://www.amazon.com/dp/B000P0R1SY/?tag=pfamazon01-20

Otherwise search the internet for "problems in mathematical analysis".

 

[member 587159]

Spivak's book "Calculus" is what you are looking for.

 

[fresh_42]

Spivak's book "Calculus" is what you are looking for.

I don't think so. Mine is full of exercises, many with solutions, and not only limits but e.g. integrals, too. Spivak is in the end just another book about calculus.

 

[member 587159]

I don't think so. Mine is full of exercises, many with solutions, and not only limits but e.g. integrals, too. Spivak is in the end just another book about calculus.

Spivak has many exercises solved in details while developing the theory, also many exercises from very easy to very difficult in the exercise section, and the exercises also have a solution manual. I don't understand your objection.

 

[fresh_42]

No objection, Spivak is a good reference. I think the OP is looking for a collection of exercises rather than an ordinary textbook. Demidovich is such a collection. Of course we cannot know for sure what he is looking for, especially as there is no such book which only covers limits of all kind. He has $\lim_{x \to 1} \dfrac{x-1}{\sin(\pi x)}$ as an example. I thought: what about $x\to 0, x\to 1/2$ and similar with every example?

Here is another collection:
http://etananyag.ttk.elte.hu/FiLeS/downloads/4b_FeherKosToth_MathAnExII.pdf

 

[Infrared]

I think mostly intro calculus books will have limit problems like that- Stewart's book is pretty widely used. @fresh_42 points out that L'Hospital is useful for some of these problems. For the limits with functions as exponents, taking logarithms (and then using L'Hopital if necessary) is another useful trick.