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)
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.