Option 7
Trig Functions Category 2: Sine Limit Identity

Definition: Sine Limit Identity

$\underset{x\to 0}{\lim }\frac{\mathit{sin}\left(\mathrm{(}x\mathrm{)}\right)}{x}=1$

OR

$\underset{x\to 0}{\lim }\frac{x}{\mathit{sin}\left(\mathrm{(}x\mathrm{)}\right)}=1$

Note:

–           The limit identity only applies for $x\to 0$.

–           The limit identity works the same no matter which format you have for the original limit.

–           The limit has the same value as long as whatever is inside the sine function, $x$, matches exactly with the piece on the other side of the fraction, $x$.

For example, $\underset{x\to 0}{\lim }\frac{\mathit{sin}\left(\mathrm{(}3x\mathrm{)}\right)}{3x}=1$