Limit of polynomial, rational and composite functions for JEE

Formula

\[\lim_{x\to a}p(x)=p(a),\qquad \lim_{x\to a}\frac{p(x)}{q(x)}=\frac{p(a)}{q(a)}\ (q(a)\neq 0),\qquad \lim_{x\to a}f(g(x))=f\!\left(\lim_{x\to a}g(x)\right)\]

Variables: \(p,q\) polynomials.

Conditions: For composition, \(f\) should be continuous at \(\lim g(x)\).

Evaluating standard limits quickly.