2) Algebraic Limits:
A) Factorization process of finding limit.
If direct substitution of x=a in a rational function takes useless form like then a factor of (x-a) can be cancelled from both numerator and denominator. Now again use direct substitution to see if limit can be evaluated.
B) Using the result
Illustration 8: Evaluate ?
C) Using rationalization:
Some factor which creates form is cancelled by rationalization and limit is evaluated.
Illustration 9: Evaluate ?
D) Limits where x®
We write down expression as a rational function and then divide each term by highest power of x obtained from numerator and denominator.
Illustration 10: Find the value of ?
3) Trigonometric Limits:
The trigonometric limits are those which involve trigonometric ratios. The use of the result is a integral part of evaluation of such limits.
Illustration 11: Evaluate ?
= 1´ p ´ 1
4) Exponential and Logarithmic Limits:
These are the limits which involve use of logarithmic and exponential functions. Some of the standard limits help us in solving these limits.
Find the following limits