MathDB

For

a>0

, let

l

be the line created by rotating the tangent line to parabola

y=x^{2}

, which is tangent at point

A(a,a^{2})

, around

A

-\frac{\pi}{6}

. Let

B

be the other intersection of

l

and

y=x^{2}

. Also, let

C

(a,0)

and let

O

be the origin. (1) Find the equation of

l

. (2) Let

S(a)

be the area of the region bounded by

OC

CA

and

y=x^{2}

. Let

T(a)

be the area of the region bounded by

AB

and

y=x^{2}

. Find

\lim_{a \to \infty}\frac{T(a)}{S(a)}

193