There is a function $f ( x )$ that is differentiable on the set of all real numbers. For all real numbers $x$, $f ( 2 x ) = 2 f ( x ) f ^ { \prime } ( x )$, and $$f ( a ) = 0 , \quad \int _ { 2 a } ^ { 4 a } \frac { f ( x ) } { x } d x = k \quad ( a > 0,0 < k < 1 )$$ When this holds, what is the value of $\int _ { a } ^ { 2 a } \frac { \{ f ( x ) \} ^ { 2 } } { x ^ { 2 } } d x$ expressed in terms of $k$? [3 points]
(1) $\frac { k ^ { 2 } } { 4 }$
(2) $\frac { k ^ { 2 } } { 2 }$
(3) $k ^ { 2 }$
(4) $k$
(5) $2 k$

In the figure, let $a$ be the area of region $A$ enclosed by the two curves $y = e ^ { x } , y = x e ^ { x }$ and the $y$-axis, and let $b$ be the area of region $B$ enclosed by the two curves $y = e ^ { x } , y = x e ^ { x }$ and the line $x = 2$. What is the value of $b - a$? [4 points]
(1) $\frac { 3 } { 2 }$
(2) $e - 1$
(3) 2
(4) $\frac { 5 } { 2 }$
(5) $e$

If $I = \sum _ { k = 1 } ^ { 98 } \int _ { k } ^ { k + 1 } \frac { k + 1 } { x ( x + 1 ) } d x$, then
[A] $I > \log _ { e } 99$
[B] $I < \log _ { e } 99$
[C] $I < \frac { 49 } { 50 }$
[D] $I > \frac { 49 } { 50 }$