Let be a positive constant number

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Let

a

be a positive constant number. Consider two curves

C_1: y = e^x

C_2: y = e^{a-x}

. Let

S

be the area of the part surrounding by

C_1

C_2

and the

Y

-axis, then

\lim_{a \to 0} \frac{S}{a^2}

equals (1) 4 (2) 1/2 (3) 0 (4) 1/4