Evaluate:

Limit (sin^-1 y * sin y – y²)/y⁶
y → 0

Bonus Question:

Work out the following limit:

Limit (tan^-1 y * tan y – y²)/y⁶
y → 0

If

f(x) = x + a x^3 + b x^5 + ...,

then

f^-1(x) = x - a x^3 + (3a^2-b) x^5 + ...,

and

lim (f(x)*f^-1(x) - x^2)/x^6 = 2a^2.

Posted by Eigenray on 2008-06-04 13:01:27