Rain English Lyrics, South Africa Benjamin, Dube 25 Comments. Refrain: Jehovah is your name x2. Mighty warrior, great in battle. Jehovah is your name. (Repeat) Mighty warrior, great in battle. Jehovah is your name.
Best Answer: You're wrong about what the arctan function is. arctan is that function that answers the question, What angle theta yields the tan (theta) = x? arctan 0 = 0 because the tan 0 = sin 0 / cos 0 = 0/1 = 0.
Now you make a simple substitution: $$t = \arctan x \implies x = \tan t$$. $$x \rightarrow 0 \implies t \rightarrow 0$$. Finally, $$\lim_{x \rightarrow 0} \frac{\arctan x}{x} = \lim_{t \rightarrow 0} \frac{t}{\tan t} = 1$$ (the last limit equals $1$, as proved above).