Question

Find the limit:

Answer 1

http://prntscr.com/38x0fu

Answer 2

@iambatman

Answer 3

Area A = Area of sector - Area of triangle OPR =
1/2 * r^2 * theta - 1/2 * r * r * sin(theta) = r^2/2( theta - sin(theta) )

Area B = 1/2 * QR * PQ = 1/2 * (r - rcos(theta)) * r * sin(theta) =
r^2/2 * (1 - cos(theta)) * sin(theta)

Area A / Area B = { r^2/2( theta - sin(theta) ) } / { r^2/2 * (1 - cos(theta)) * sin(theta) } = ( theta - sin(theta) ) / (1 - cos(theta)) * sin(theta)

lim theta->0+ is 0/0. Apply L'H rule.

Answer 4

Alright, thank you very much for your help :)

Answer 5

You are welcome.

Answer 6

I am getting 1/3. But have not double-checked it.

Answer 7

Yup, it was 1/3 :)