Continuity

$\lim↙{x→0} {sinx}/{x} = 1$

$\lim↙{x→0} {tanx}/{x} = 1$

$\lim↙{x→0} cosx = 1$

$\lim↙{x→0} {a^x – 1}/{x} = log a$

$\lim↙{x→0} log (1+x)^{1/x} = log e$


$\lim↙{x→0} (1+x)^{1/x} = e $

Note: Whenever there is a role of π with x e.g. ${sinπx}/{x – 1} + a$
Put x – 1 = h i.e. Make denominator singular