MATHEMATICAL WORLD

LIMIT 1. DEFINITION : Let \(\mathrm{f}(\mathrm{x})\) be defined on an open interval about 'a' except possibly at 'a' itself. If \(\mathrm{f}(\mathrm{x})\) gets arbitrarily close to \(\mathrm{L}\) (a finite number) for all \(\mathrm{x}\) sufficiently close to 'a' we say that \(\mathrm{f}(\mathrm{x})\) approaches the limit \(\mathrm{L}\) as \(\mathrm{x}\) approaches 'a' and we write \(\displaystyle \lim_{x \rightarrow a} f(x)=L\) and say "the limit of \(f(x)\) , as \(\mathrm{x}\) approaches a, equals \(\mathrm{L}\) ". All Chapter Notes, Concept and Important Formula 2. LEFT HAND LIMIT & RIGHT HAND LIMIT OF A FUNCTION: Left hand limit \((\mathrm{LHL})=\displaystyle \lim_{\mathrm{x} \rightarrow \mathrm{a}^{-}} \mathrm{f}(\mathrm{x})=\displaystyle \lim_{\mathrm{h} \rightarrow 0} \mathrm{f}(\mathrm{a}-\mathrm{h}), \mathrm{h}>0\) Right hand limit \((\mathrm{RHL})=\displaystyle \lim_{\mathrm{x} \rightarrow \mathrm{a}^{+}} \mathrm{f}...