Barrons AP Calculus

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The left    Riemann Sum with    8   equal   subintervals.

The midpoint    Riemann Sum with    8   equal   subintervals.

The trapezoidal approximation   with    8   equal   subintervals.

The  table   shows   some    values  of  a   differentiable  function   f    and     its

derivative  f   ′:

Find    .

5

6

11.5

14

The solution    of  the differential    equation        for which   y   =   −1  when

x   =   1   is

ln  y^2     =   x^2     −   1   for all x