[問題] 微積分(誰會解?)
1. Find the area of largest rectangle that can be inscribed in a semicircle
of radius r.
2. Evaluate the integral
1 1 ________
a) ∫ ∫ √x^3 + 1 dxdy
0 √y
0
b) ∫ xe^x dx
-∞
tanx － x
3. Find lim ─────
x→0 x^3
4. Find the equations of the tangent plane and the normal line to the surface
sin(xyz) ＝ x+2y+3z at the point (2,-1,0)
5. Find the radius of convergence and interval of convergence of series
∞ (-3)^n · x^n
Σ ───────
n＝0 √(n+1)
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