How would one work out this limit?
lim 48(sum(x^n/n! -x -1))/x^2
x->0
im sorry for the formatting... thanks in advance
If you mean $\displaystyle \lim_{x \to 0} \frac{48}{x^2} \left( \sum_{n=0}^{\infty} \frac{x^n}{n!} - 1 - x\right) $
it's $\displaystyle \lim_{x \to 0} \frac{48}{x^2} \left(1 +x + \frac{x^2}{2!} + \frac{x^3}{3!} \cdots - 1 - x\right) = \lim_{x \to 0} \frac{48}{x^2} \left(\frac{x^2}{2!} + \frac{x^3}{3!} \cdots \right) $ = $\displaystyle \lim_{x \to 0} 48 \left(\frac{1}{2!} + \frac{x}{3!} \cdots \right) =24$