Algebra of limits for JEE

Formula

\[\begin{aligned}\lim(f\pm g)&=\lim f\pm \lim g,\\ \lim(cf)&=c\lim f,\\ \lim(fg)&=(\lim f)(\lim g),\\ \lim\left(\frac{f}{g}\right)&=\frac{\lim f}{\lim g}\quad (\lim g\neq 0)\end{aligned}\]

Variables: Limits are taken as \(x\to a\).

Conditions: Assuming the individual limits exist and denominator limit is nonzero for quotient.

Direct evaluation of limits.