Barrons AP Calculus

and the magnitude   of  the acceleration,   |a|,    is  given   by

(B)

By  the Ratio   Test    the series  converges   when

Checking    the endpoints,  we  find:

    is  the alternating harmonic    series, which   converges.

    is  the harmonic    series, which   diverges.

Hence   the interval    of  convergence is  0   ≤ x <   2.

(C)

(C) We  integrate   by  parts   using   u   =   ln  x,  dv  =   dx; then    du  =    dx,    v   =   x,

and