Question

what is the limit of sqrt(1-costheta)/sin3theta as x approaches 0 from the positive side?

Answer 1

sqrt?

Answer 2

square root

Answer 3

just testing anyone who's taking up engineering :D

Answer 4

\[=\lim_{x \rightarrow 0} \frac{ \sqrt{1-\cos(x)} }{\sin(3x)} = \lim_{x \rightarrow 0} \frac{ \frac{d}{dx} [ \sqrt{1-\cos(x)} ] }{ \frac{d}{dx} \sin(3x)}\]

Answer 5

=\[\lim_{x \rightarrow 0} \frac{ \frac{\sin(x)}{2\sqrt{1-\cos(x)} }} {3\cos(3x)}\]

Answer 6

\[= \frac{1}{6}\lim_{x \rightarrow 0} \frac{\sin(x)}{\cos(3x)\sqrt{1-\cos(x)}}\]

Answer 7

etc it just keeps repeating, doesn't exist.

Answer 8

This question is vague. You're looking for the limit of this function as x approaches zero but your variabes consist of theta. Therefore, the answer is the question itself