## Calculus 8th Edition

$-\infty$
Find the limit $\lim\limits_{x \to 3^{+}}log_{10}(x^{2}-5x+6)$ This is quadratic equation in the powers of 2 with roots $(x-2)$$(x-3)$. $\lim\limits_{x \to 3^{+}}log_{10}(x^{2}-5x+6)=\lim\limits_{x \to 3^{+}}log_{10}(x-2)(x-3)$ The limit of the logarithm base 10 of $x$ when $x$ approaches zero from the positive side (0+) is minus infinity. This implies $\lim\limits_{x \to 3^{+}}log_{10}(x^{2}-5x+6)=-\infty$