Lim x - 12 x-3-x-1-3 x2-3 x-6

Lim_x → 1(2x 3)(√(x) 1)/3x^2+3x 6 [It is of (0/0) form] =lim_x → 1(2x 3)(√(x) 1)/3[x^2+x 2] [It is of (0/0) form] =lim_x → 1(2x 3)(√(x) 1)/[x^2+2x x 2]=lim_x → ...

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 → 12 x-...

Question

${lim}_{x \to 1} \frac{(2 x - 3) (\sqrt{x} - 1)}{3 x^{2} + 3 x - 6}$

Open in App

Solution

${lim}_{x \to 1} \frac{(2 x - 3) (\sqrt{x} - 1)}{3 x^{2} + 3 x - 6}$ [It is of $(\frac{0}{0})$ form]

$= {lim}_{x \to 1} \frac{(2 x - 3) (\sqrt{x} - 1)}{3 [x^{2} + x - 2]}$ [It is of $(\frac{0}{0})$ form]

$= {lim}_{x \to 1} \frac{(2 x - 3) (\sqrt{x} - 1)}{[x^{2} + 2 x - x - 2]} = {lim}_{x \to 1} \frac{(2 x - 3) (\sqrt{x} - 1)}{3 (x + 2) (x - 1)}$

$= {lim}_{x \to 1} \frac{(2 x - 3) (\sqrt{x} - 1)}{3 (x + 2) (\sqrt{x - 1}) (\sqrt{x} + 1)}$ [It is of $(\frac{0}{0})$ form]

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

$= \frac{(2 - 3)}{3 (1 + 2) (1 + 1)} = \frac{- 1}{3 \times 3 \times 2} = - \frac{1}{18}$

Suggest Corrections

Similar questions

lim x \to 1 \frac{(2 x - 3) (\sqrt{x} - 1)}{3 x^{2} + 3 x - 6}

Q. Solve

lim x \to 1 \frac{(2 x - 3) (\sqrt{x} - 1)}{3 x^{2} + 3 x - 6}

Q. Solve :

{lim}_{x \to 1} \frac{(2 x - 3) (\sqrt{x} - 1)}{3 x^{2} + 3 x - 6}

Q. Evaluate the following one sided limits:

(i)

\lim_{x \to 2^{+}} \frac{x - 3}{x^{2} - 4}

(ii)

\lim_{x \to 2^{-}} \frac{x - 3}{x^{2} - 4}

(iii)

\lim_{x \to 0^{+}} \frac{1}{3 x}

(iv)

\lim_{x \to - 8^{+}} \frac{2 x}{x + 8}

(v)

\lim_{x \to 0^{+}} \frac{2}{x^{1 / 5}}

(vi)

\lim_{x \to \frac{π}{2}} \tan x

(vii)

\lim_{x \to - π / 2^{+}} \sec x

(viii)

\lim_{x \to 0^{-}} \frac{x^{2} - 3 x + 2}{x^{3} - 2 x^{2}}

(ix)

\lim_{x \to - 2^{+}} \frac{x^{2} - 1}{2 x + 4}

(x)

\lim_{x \to 0^{-}} 2 - \cot x

(xi)

\lim_{x \to 0^{-}} 1 + cosec x

\lim_{x \to 1} \frac{x^{3} + 3 x^{2} - 6 x + 2}{x^{3} + 3 x^{2} - 3 x - 1}

Join BYJU'S Learning Program

limx→1(2x−3)(√x−1)3x2+3x−6

${lim}_{x \to 1} \frac{(2 x - 3) (\sqrt{x} - 1)}{3 x^{2} + 3 x - 6}$