1. Find the volume of solids obtained by rotating the region bounded by
the given curve about the y-axis:y=1/x, x=0, y=1/2, y=1
2. Is the following definite integral convergent or divergent?
And prove your result.
∞ 1
∫ --------- dx (分母是雙重根號)
1 √x＋√x
3. Rotate the region bounded by y=2, x=0, y=0, and y=ln x about the y-axis.
Compute the volume of the resulting solid.
4. Evaluate tan(2x)
lim (tanx) (0<x<π/4)
x->(π/4)
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