Question

Evaluate
$\rm \displaystyle \lim_{n\to 5}\ \frac{x^{2}-9x+20}{x^{2}-6x+5}$

Answer 1

Solution :

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i ) x² - 9x + 20

Splitting the middle term , we get

= x² -5x - 4x + 20

= x( x - 5 ) - 4( x - 5 )

= ( x - 5 )( x - 4 ) ----( 1 )

ii ) x² - 6x + 5

= x² -5x - 1x + 5

= x( x - 5 ) -1( x - 5 )

= ( x - 5 )( x - 1 ) -----( 2 )

iii ) (x²-9x+20)/(x²-6x+5)

= [(x-5)(x-4)]/[(x-5)(x-1)]

After cancellation, we get

= (x-4)/(x-1) ---( 3 )
___________________

Here ,

$\rm \displaystyle \lim_{x\to 5}\ \frac{x^{2}-9x+20}{x^{2}-6x+5}$

= $\rm \displaystyle \lim_{x\to 5}\ \frac{x-4}{x-1}$
=$\rm \displaystyle \frac{5-4}{5-1}$

= 1/4

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