Question

limit x approaches 1 ( underootx - 1) (2x - 3) / 2x^2 +x -3

Answer 1

Heya user,

Firstly, [ √x - 1 ][ 2x - 3 ]/ [ 2x² + x - 3 ]
==== [ √x - 1 ][ 2x - 3 ] / [ ( 2x + 3 )(√x + 1 )( √x - 1 ) ]
==== [ 2x - 3 ] / [ ( 2x + 3 ) (√x + 1) ] ---> (1)

Now, for limits, we substitute : x = 1 in (1) ::--->

$\lim_{x \to \(1} [\sqrt{x} - 1 ][ 2x - 3 ] / [ 2 x^{2} + x - 3]$
= $\lim_{x \to \(1} [ 2x - 3 ] / [ ( 2x + 3 ) ( \sqrt{x} + 1) ]$ = -1/10
--->You got your answer