Evaluate:-

lim (x^{3}+3x^{2}-9x-2)/(x^{3}-x-6)

x --2

which is of the form 0/0.

factorise the polynomial as (x-2) is a common factor of both numerator and denominator.

$=\underset{x\to 2}{lim}\frac{(x-2)({x}^{2}+5x+1)}{(x-2)({x}^{2}+2x+3)}\phantom{\rule{0ex}{0ex}}=\frac{{2}^{2}+5*2+1}{{2}^{2}+2*2+3}\phantom{\rule{0ex}{0ex}}=\frac{15}{11}$

this can be done by L'HOSPITAL rule also:

differentiate the numerator and denominator and substitute the value of x as 2.

hope this helps you.

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