Lim x - 31-x-3-2-x2-4 x-3

Lim_x → 3 ( 1/x 2 2/x^2 4x+3 ) =lim_x → 3 ( 1/x 3 2/(x 3)(x 1) ) =lim_x → 3 ( x 1 2/(x 3)(x 3) ) =lim_x → 3 ( x 3/(x 1)(x 3) ) [It is of (0/0) form] =lim_x → 31 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

lim x → 31/x-...

Question

${lim}_{x \to 3} (\frac{1}{x - 3} - \frac{2}{x^{2} - 4 x + 3})$

Open in App

Solution

${lim}_{x \to 3} (\frac{1}{x - 2} - \frac{2}{x^{2} - 4 x + 3})$

$= {lim}_{x \to 3} (\frac{1}{x - 3} - \frac{2}{(x - 3) (x - 1)})$

$= {lim}_{x \to 3} (\frac{x - 1 - 2}{(x - 3) (x - 3)})$

$= {lim}_{x \to 3} (\frac{x - 3}{(x - 1) (x - 3)})$ [It is of $(\frac{0}{0})$ form]

$= {lim}_{x \to 3} \frac{1}{x - 1}$

$= \frac{1}{3 - 1}$

$= \frac{1}{2}$

Suggest Corrections

Similar questions

Evaluate

l i m_{x \to - 3} (\frac{1}{x^{2} + 4 x + 3} + \frac{1}{x^{2} + 8 x + 15})

${lim}_{x \to 3} (\frac{1}{x - 3} - \frac{3}{x^{2} - 3 x})$

lim x \to \infty {(\frac{x^{2} + 5 x + 3}{x^{2} + x + 3})}^{1 / x}

$lim x \to \infty (\frac{5 x^{2} + x + 3}{x^{2} + x + 3})^{\frac{1}{x}}$
(2002)

{lim}_{x \to 3} (\frac{1}{x - 3} + \frac{9 x}{27 - x^{2}}) .

Join BYJU'S Learning Program

limx→3(1x−3−2x2−4x+3)

limx→3(1x−2−2x2−4x+3) =limx→3(1x−3−2(x−3)(x−1)) =limx→3(x−1−2(x−3)(x−3)) =limx→3(x−3(x−1)(x−3)) [It is of (00) form] =limx→31x−1 =13−1 =12

${lim}_{x \to 3} (\frac{1}{x - 3} - \frac{2}{x^{2} - 4 x + 3})$