displaystyle limx → 1 ((√x-1)(2x-3)/2x2+x-3) is

Question

displaystyle limx → 1 ((√x-1)(2x-3)/2x2+x-3) is (A) (1/10) (B) (-1/10) (C) 1 (D) None of these

Tardigrade Admin · Accepted Answer

We have, displaystyle limx → 1 ((√x-1)(2x-3)/2x2+x-3) = displaystyle limx → 1 ((√x-1)(2x-3)/(x-1)(2x+3)) = displaystyle limx → 1 ((2x-3)/(2x+3)) × displaystyle limx → 1 ((x(1/2)-1(1/2)/x-1)) =(-1/5) ×(1/2)(1)-(1/2) =(-1/5)×(1/2)=(-1/10)

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

$\frac{1}{10}$

$\frac{- 1}{10}$

$1$

None of these

Q. x→1lim​ 2x2+x−3(x​−1)(2x−3)​ is

101​

10−1​

1

None of these

We have, x→1lim​ 2x2+x−3(x​−1)(2x−3)​ =x→1lim​ (x−1)(2x+3)(x​−1)(2x−3)​ =x→1lim​ (2x+3)(2x−3)​×x→1lim​ (x−1x21​−121​​) =5−1​×21​(1)−21​ =5−1​×21​=10−1​

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

$\frac{1}{10}$

$\frac{- 1}{10}$

$1$