Question

what's lim x-0(x^(2)tan^(2)(cos^(-1)X)?

Answer 1

Well, I guess we would tan(arccosx) into sines and cosines:

\[\frac{ x^{2}\sin(arccosx) }{ \cos(arccosx) }\]cos(arccosx) just cancels to x. And then that resulting x cancels out with one of the x's on top to leave:
\[xsin(arccosx)\]Now that we have this, theres nothing undefined to even worry about. Plug in 0 and the limit gives you 0