Displaystyle lim-xrightarrow 1-frac-left - 2x-3 right -left - sqrt-x-1 right -2x-2-x-3- is displaystyle frac-1-b- Find b

Question

Toppr Admin · Accepted Answer

Limx-x2192-1-2x-x2212-3-x221A-x-x2212-1-2x2-x-x2212-3-limx-x2192-1-2x-x2212-3-x221A-x-x2212-1-2x-3-x-x2212-1-limx-x2192-12x-x2212-3-2x-3-x221A-x-1-2-x2212-3-2-3-1-1-x2212-110-x21D2-b-10

$lim x \to 1 \frac{(2 x - 3) (\sqrt{x} - 1)}{2 x^{2} + x - 3} .$ is $\frac{- 1}{b}$ Find b

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

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

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

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

$= - \frac{1}{10}$

$\Rightarrow b = 10$

limx→1(2x−3)(√x−1)2x2+x−3. is −1b Find b

limx→1(2x−3)(√x−1)2x2+x−3=limx→1(2x−3)(√x−1)(2x+3)(x−1)=limx→12x−3(2x+3)(√x+1)=2−3(2+3)(1+1)=−110⇒b=10

$lim x \to 1 \frac{(2 x - 3) (\sqrt{x} - 1)}{2 x^{2} + x - 3} .$ is $\frac{- 1}{b}$ Find b

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

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

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

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

$= - \frac{1}{10}$

$\Rightarrow b = 10$