Question

Lim ( y 3 – y 2 – y -2 )

y – 2 2y 3 – 5y 2 + 5y – 6

Answer 1

Question:

$=\boxed{\lim\limits_{y \to 2}{y^3-y^2-y-2\over 2y^3-5y^2+5y-6}}$

after putting value of y as to we get form $0\over0$ of so,

we can solve this by two methods

1) L HOPITAL'S RULE

2)Factorization method

we solve by factorization method

first we take out common factor from both denominator and numerator,

${\lim\limits_{y \to 2}{y^3-y^2-y-2\over 2y^3-5y^2+5y-6}}$

${\lim\limits_{y \to 2}{y^3-y^2-y-2\over 2y^3-5y^2+5y-6}}=\lim\limits_{y \to 2}{(y-2)(y^2+y+1)\over(y-2)(2y^2-y+3}$

as (y-2) is a conman factor in both numerator and denominator we cancel it out,

$=\lim\limits_{y \to 2}{\cancel{(y-2)}(y^2+y+1)\over\cancel{(y-2)}(2y^2-y+3}$

$=\lim\limits_{y \to 2}{(y^2+y+1)\over)(2y^2-y+3}$

now, putting value of y as 2 in equation (1)

we ge limit $\boxed{limit={7\over 9}}$ as our answer.