31.
32.
33.
34.
Part B
(A) Use the Ratio Test:
which equals zero if x ≠ 1. The series also converges if x = 1 (each term
equals 0).
(B) The absolute value function f(x) = |x| is continuous at x = 0, but f ′(0)
does not exist.
(B) The Maclaurin series is
When an alternating series satisfies the Alternating Series Test, the sum
is approximated by using a finite number of terms, and the error is less
than the first term omitted. On the interval − π x π, the maximum
error (numerically) occurs when x = π. Since
four terms will suffice to assure no error greater than 0.1.
(D) S is the region bounded by y = sec x, the y-axis, and y = 4.
We revolve region S about the x-axis. Using washers, ΔV = π(R^2 − r^2 ) Δx
