Hello, I have a problem with which I seem to be getting nowhere. I have to find the value of the limit, and the answer says that it is 3/2
lim 5x^2-7x+2/x^2-1
lim x-> 1
Thanks for the help.
Notice that
$\displaystyle 5x^2 - 7x + 2 = (5x - 2)(x - 1)$ and $\displaystyle x^2 - 1 = (x + 1)(x - 1)$.
So $\displaystyle \frac{5x^2 - 7x + 2}{x^2 - 1} = \frac{(5x - 2)(x - 1)}{(x + 1)(x - 1)}$
$\displaystyle = \frac{5x - 2}{x + 1}$.
Therefore
$\displaystyle \lim_{x \to 1} \frac{5x^2 - 7x + 2}{x^2 - 1} = \lim_{x \to 1} \frac{5x - 2}{x + 1}$
$\displaystyle = \frac{5(1) - 2}{1 + 1}$
$\displaystyle = \frac{3}{2}$.
Notice that the reason you could not just set x= 1 and evaluate is because both numerator and denominator are equal to 0 when x= 1. You should then recognize that if a polynomial is 0 at x= a, (x- a) is a factor. Recognizing that x-1 must be a factor of $\displaystyle 5x^2- 7x+ 2$ you can just divide it by x-1 to find the other factor.