utefdxd的部落格

標題:

find limit

發問:

let F(y)=Integrate{[(sin(y/2))^2-(sin(x/2))^2]^(-0.5), 0, y}dx find the limit of F(y) as y tends to 0.

• FORM 2 MATHS@1@
• O形腳的英文是甚麼-
• O'Neill (急)@1@

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最佳解答:

Integrate{[(sin(y/2))^2-(sin(x/2))^2]^(-0.5), 0, y}dx Consider y=+0 In the integral interval, 00 cos(x/2)->1 (2) becomes Integrate{2, 0, 兀/2}dz = 兀 I believe the case for y=-0 should be similar

其他解答:

To: 螞蟻雄兵 No, the answer is not F(0) because discontinuity occurs at y=0. Actually, the answer is Pi, but I do not know how to prove it rigorously. Can any body help? Maybe you can try to find F(0.1), F(0.01), F(0.001), ... by numerical method, verifying the answer(Pi) But try to prove it.