the trapezoid are 24 − 2x and , and the height is .
The volume of the trough (in in.^3 ) is given by
Since , the maximum volume is attained by folding the
metal 8 inches from the edges.
(a) Both π/4 and the expression in brackets yield 0.7853981634, which is
accurate to ten decimal places.
(b)
(c) 4 tan−^1 tan−^1 = 0.7854; this agrees with the value of to four
decimal places.
(d) The series
converges very slowly. Example 56, evaluated the sum of 60 terms of the
series for π (which equals 4 tan−^1 1). To four decimal places, we get π =
3.1249, which yields 0.7812 for π/4—not accurate even to two decimal
places.
(a) The given series is alternating. Since . Since
ln x is an increasing function,
