Question

lim x tendes to 1 1/x-3 -3/x(x-3)(x-2)​

Answer 1

The question can be done in the above

method

$if \: u \: substitute \: the \: value \\of\: x=1 \:there\: is\: no \: \dfrac{ \alpha }{ \alpha } or \dfrac{0}{0} or \: any \: other \: undefined \\ form \: so \: u \: can \: directly \\ substitute \: u \: will \: get \: the \\ same \: answer \: but \: if \: u \\ substitute \:and \: it \: is \: in \: the \\ undefined \: form \: u \: need \: to \: use \\ the \: method \: as \: i \: used$

Substituting x=1

$= \dfrac{1}{1 - 3} - \dfrac{3}{1(1 - 3)(1 - 2)}$

$\dfrac{ - 1}{2} - \dfrac{ - 3}{2}$

$= \dfrac{ - 4}{2} = - 2$