Limx→1(2x−3)(x−1)2x2+x−3=

limx→1 (2x−3)(x−1)2x2+x−3=limx→1 (2x−3)(x−1)2x2+3x−2x−3=limx→1 (2x−3)(x−1)x(2x+3)−1(2x+3)=limx→1 (2x−3)(x−1)(2x+3)(x−1)=limx→1 (2x−3)(x−1)(2x+3)(x+1)(x−1)=limx→1 (2x−3)(2x+3)(x+1)=−1(5)(2)

Limx→1(2x−3)(x−1)2x2+x−3=

limx→1 (2x−3)(x−1)2x2+x−3=limx→1 (2x−3)(x−1)2x2+3x−2x−3=limx→1 (2x−3)(x−1)x(2x+3)−1(2x+3)=limx→1 (2x−3)(x−1)(2x+3)(x−1)=limx→1 (2x−3)(x−1)(2x+3)(x+1)(x−1)=limx→1 (2x−3)(2x+3)(x+1)=−1(5)(2)

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

$\underset{x \to 1}{L i m} \frac{(2 x - 3) (\sqrt{x} - 1)}{2 x^{2} + x - 3} =$

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$\frac{1}{10}$

$- \frac{1}{10}$

$\frac{2}{5}$

$- \frac{2}{5}$

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\begin{array}{l} lim_{x \to 1} \frac{(2 x - 3) (\sqrt{x - 1})}{2 x^{2} + x - 3} \\ = lim_{x \to 1} \frac{(2 x - 3) (\sqrt{x} - 1)}{2 x^{2} + 3 x - 2 x - 3} \\ = lim_{x \to 1} \frac{(2 x - 3) (\sqrt{x} - 1)}{x (2 x + 3) - 1 (2 x + 3)} \\ = lim_{x \to 1} \frac{(2 x - 3) (\sqrt{x} - 1)}{(2 x + 3) (x - 1)} \\ = lim_{x \to 1} \frac{(2 x - 3) (\sqrt{x} - 1)}{(2 x + 3) (\sqrt{x} + 1) (\sqrt{x} - 1)} \end{array}$