Answer
The maximum value of $~~h~~$ is $~~\frac{25L}{24}$
Work Step by Step
In part (a), we found that $a_1 = \frac{L}{2}$
In part (b), we found that $a_2 = \frac{L}{4}$
In part (c), we found that $a_3 = \frac{L}{6}$
In part (d), we found that $a_4 = \frac{L}{8}$
We can find the maximum value of $h$:
$h = a_1+a_2+a_3+a_4$
$h = \frac{L}{2}+\frac{L}{4}+\frac{L}{6}+\frac{L}{8}$
$h = \frac{25L}{24}$
The maximum value of $~~h~~$ is $~~\frac{25L}{24}$
