Generating...                               part5_n0

  1. $\displaystyle \frac{ \cos \theta} { \sin \theta\, \cot(\theta ) } = 1 $ is an identity and is true for all values of $\theta$ in the set

    $\displaystyle\left\{\theta \,\left\vert\, -\infty < \theta < \infty \right.\right\}$

    $\displaystyle\left\{\theta \,\left\vert\, \theta \neq {{\pi\,n}\over{2}} ,\,n \mbox{ is an integer},\, \theta \in (-\infty,\infty)\right.\right\}$

    $(0,2\pi)$

    $\displaystyle\left\{\theta \,\left\vert\, \theta \neq {{\pi\,\left(2\,n+1\r... ...{2}} ,\,n \mbox{ is an integer},\, \theta \in (-\infty,\infty)\right.\right\}$

    $\displaystyle\left\{\theta \,\left\vert\, \theta \neq \pi\,n ,\,n \mbox{ is an integer},\, \theta \in (-\infty,\infty)\right.\right\}$

  2. If $\displaystyle f\left(x\right)=\sqrt{x}$ and $g(x)=\displaystyle {{1}\over{x^2-36}}$, then the domain of $f$ composite $g$, $(f \circ g)(x)$, is

    $\displaystyle \left\{x\,\left\vert\,x\neq 36, x \mbox{ is a nonnegative real number}\right.\right\}$

    $\displaystyle (-\infty, -6) \cup (6, \infty)$

    $(0, 6) \cup ( 6,\infty)$ $\left\{x\,\left\vert\,x\ge0,\, x \in (-\infty,\infty)\right.\rigth\}$

    All real numbers


Department of Mathematics
Last modified: 2025-05-04