Answer
$\lim\limits_{p \to -1} f(x) = 0.6$
Work Step by Step
$\lim\limits_{p \to -1} \frac{1+p^{9}}{1+p^{15}}$
Chose numbers close to -1.
$x | f(x)$
$-0.95 | 0.68$
$-0.99 | 0.62$
$-0.9999 | 0.60$
$-0.99999 | 0.60$
$-0.9999999 | 0.60$
$\lim\limits_{p \to -1^{-}} \frac{1+p^{9}}{1+p^{15}} = 0.60$
$x | f(x)$
$-1.5| 0.086$
$-1.1| 0.43$
$-1.01| 0.58$
$-1.001| 0.60$
$-1.00001| 0.60$
$\lim\limits_{p \to -1^{+}} \frac{1+p^{9}}{1+p^{15}} = 0.60$
By the table of numbers it appears that $\lim\limits_{p \to -1^{-}} f(x) = 0.60$ and $\lim\limits_{p \to -1^{+}} f(x) = 0.60$.
So $\lim\limits_{p \to -1} f(x) = 0.60$.
