Question

Evaluate
$\rm \displaystyle \lim_{n\to 2}\ \frac{x-2}{x^{2}+x-6}$

Answer 1

Solution :

i ) x² + x - 6

Splitting the middle term ,we get

= x² + 3x - 2x - 6

= x( x + 3 ) - 2( x + 3 )

= ( x + 3 )( x - 2 ) ----( 1 )

Now ,

$\rm \displaystyle \lim_{n\to 2}\ \frac{x-2}{x^{2}+x-6}$

= $\rm \displaystyle \lim_{n\to 2}\ \frac{x-2}{(x+3)(x-2)}$

[ from ( 1 ) ]

= $\rm \displaystyle \lim_{n\to 2}\ \frac{1}{(x+3)}$

= 1/(2+3)

= 1/5

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