Evaluation of Limits

To facilitate the job of evaluation of limits, we divide the problems on limits in to the following categories :

(i)  Algebraic Limits, (ii) Non – Algebraic Limits

If a problem on limits does not involve trigonometric, inverse trigonometric, exponential and logarithmic functions, then it is a problem on algebraic limits. Otherwise it is a problem on non-algebraic limits.

lim x² -1, lim √(5x + 1),  lim/x→2   (5x² + 2x+1/ 3x²+x+2)

x→2       x→0

to evaluate the algebraic limits we have of algebraic limits.

I – Direct Substitution method   II – Factorisation methods:

III – Rationalisation method        IV – Method of evaluating the algebraic limits when x→0

V – Using some standard results.