[微積]
1 1
1. 若 ∫------------------ dx = 1, for some k
0 ( x^2 + k^2 )^2
1 x - 1 + k
則 ∫------------------ dx = ?
-1 ( x^2 + k^2 )^2
2. Define f(x) = e^(-1/x^2) if x ≠ 0
= 0 if x = 0
(1)Find f'(0) (2)Is f'(x) continuous at x = 0?
2n 2
arcsin(x) ∞ 2 (n!) 2n+1
3.Show that ----------- = Σ ---------- x ,
sqrt(1-x^2) n=0 (2n+1)!
For all |x| < 1.
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