I have this limit:
$\lim_{x \to 1} \frac{2x^2-x-6}{x(x-1)^3}$
This can be written as:
$\lim_{x \to 1^+} \approx \frac{-5}{1\times\mbox{tiny positive}} \to - \infty$
Why is that? I mean, let's plug in some numbers. $-5/1.0000000001$ is almost $-5$ , the greater the denominator becomes the close the number to $-5$
Can anybody tell me why the book says it goes to -infinity? Thanks a lot