Question

what is the limit as x approaches 0 of cos(x)/(sin(x)-3))

Answer 1

Try evaluating at the point first.

\[\lim_{x\to 0} \frac{\cos(x)}{sin(x)-3} = \frac{\cos(0)}{\sin(0)-3} \]

What does
\[ \cos(0) =? \\ \sin(0) = ?\]

Answer 2

is that really all i do?

Answer 3

so it would be -1/3?

Answer 4

Done. Yup, always try to substitute before anything else. If a function is continuous at that point, it will return a real number. If it doesn't return a real number, than you may have to do more work.