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AP Calculus AB-BC 2 Pre-Final-Exam Prep Hour
Name
* BC Only
1.
d
dx [f(x)] = 2y - 4x. f(1) = 3. Use Euler's Method to approximate f(3) using 4 equal steps.
7
3
2.
Let R be the region in the first quadrant bounded by the y-axis and the graphs of y = 4x - x3 + 1 and y = 4 x.
2a.
Find the area of R.
4.515
2b.
Find the volume of the solid generated when R is revolved about the x-axis.
18.291π
2c.
R is the base of a Solid whose cross-sections perpendicular to the x-axis are semi-circles. Find the
volume of this solid.
4.653
3*.
3
⌠
⌡x cos 2x dx =
1 3
3 2
3
3
2 x sin 2x + 4 x cos 2x - 4 x sin 2x - 8 cos 2x + C
4*.
⌠ x2 - 4x + 7 dx
x3 - x2 + x + 3
⌡
1
2 ln x + 1 - 2 ln x2 - 2x + 3 + C
|
5.
|
|
y = f(x), f(0) = 3,
|
dy
= x2y – x2 . Solve the differential equation for the particular solution of f(x).
dx
3
y = 2e1/ 3 x + 1
6.
The Velocity, v, of an object is v(t) = 6t2 - 6t + 7. The Position,s, of the object is 32 when the time, t, is
2. Find the position, s, of the object when t is 3.
62