I was posed this problem on another forum by a first year and for some reason I'm struggling
lim x-> 1 from the left of
$\displaystyle (1-2x)/(x^2-1)$
Could someone provide me a precise way to show the limit goes to infinity?
I use a theorem : let $\displaystyle {x_k}->1$ from left as k->infinite , and f be continuous if $\displaystyle {f(x_k)}->infinite$ , $\displaystyle limf(x)=infinite$as $\displaystyle x->1^-$
clearly , $\displaystyle (1-2x)/(x^2-1)$ is a continuous on $\displaystyle (-infinite , 1^-)$ and let $\displaystyle {x_k}={(k-1)/k}$converges to 1 from left.
And $\displaystyle f(x_k)={(k^2)/2}-k/(4k-2)$ this is infinite as k->infinite