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 x^{2} -1, lim √(5x + 1), lim/x→2 (5x^{2} + 2x+1/ 3x^{2}+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.