Limits - Things to Keep in Mind

Limits – 3 Things to keep in mind while solving limits:

1) L’Hospital’s Rule – It is extremely important. Apply it as much as you can. Questions from this chapter are usually straight forward and simple. You just have to figure out the zero by zero form or the infinity by infinity form and apply L’Hospital’s rule. The variety of questions is large.



2) Greatest Integer Function [ . ] – To solve such questions, you need to know series expansion.
e.g.,, where [ . ] is gif.

Here, series expansion of sin(x) is,

        so, sin x / x = 1 –  x² / 3! + ...

hence,
        sin x / x < 1

3) Square root & | | - This is applicable everywhere. While solving roots or modulus, you should check for Left-Hand Limit and Right-Hand Limit. Many a times limit does not exists and questions are only given to trick you.

Books - Best book for solving limits is Arihant differential calculus by Amit M. Agrawal