The figure shows two regions in the first quadrant: A(t) is the area under the curve y=sin(x2) from 0 to t, and B(t) is the area of the triangle with vertices O, P, and it, t, 0. Find limt0+[A(t)/B(t)].
To find: The limit of the expression .
Given: The expression is
Formulae used: L’Hospital rule
For a given problem , if the limits of and are or and if the limit of their derivatives is an extended real umber, then The L’ Hospital rule .
The area under the curve from to is
And the area of the triangle with vertices O, P, and is