## Calculus with Applications (10th Edition)

$(-\infty, \infty)$
The domain is the set of all possible values of x for which the value f(x) exists (is defined). For f(x) to be defined, the following conditions must be met: 1. The radicand $\displaystyle \frac{5}{x^{2}+36}$ must not be negative (because of the square root) The numerator is positive. The denominator is $\geq$36, because $x^{2} \geq 0$, So, it is positive. The first condition is satisfied by all real numbers. 2. The denominator, $x^{2}+36$, must not be zero. We already concluded that $x^{2}+36 \geq 36 > 0$, so this condition is also satisfied by all real numbers. Domain: $\mathbb{R}$ (all real numbers) or $(-\infty, \infty)$