高数极限，请问这道题最后答案是多少? 最后一步答案怎么得到的，不太理解 高数极限？
\u8003\u7814\u9ad8\u7b49\u6570\u5b66 \uff0c\u8fd9\u9053\u9898\u6700\u540e\u7b54\u6848\u600e\u4e48\u7b97\u51fa\u6765\u7684\u8fd9\u4e2a\u662f\u8d85\u8d8a\u79ef\u5206\uff0c\u4e00\u822c\u5c31\u662f\u76f4\u63a5\u4f5c\u4e3a\u5b9a\u7406\u3002\u4e0b\u9762\u5199\u4e00\u4e2a\u222b(-\u221e\u2192\u221e) e^(-x²) dx\u7684\u7b97\u6cd5\u3002
(\u4ee5\u4e0b\u8bbe\u7684\u672a\u77e5\u6570\u8ddf\u4f60\u9898\u76ee\u4e2d\u672a\u77e5\u6570\u6ca1\u5173\u8054\u3002)
\u89e3\uff1a\u79ef\u5206\u57df\u4e3a x \u2208(-\u221e\uff0c+\u221e)
\u4ee4\uff1a F = (-\u221e\uff0c+\u221e)\u222be^(-2x²)dx
\u540c\u6837 F= (-\u221e\uff0c+\u221e)\u222be^(-2y²)dy
\u7531\u4e8ex,y\u662f\u4e92\u4e0d\u76f8\u5173\u7684\u7684\u79ef\u5206\u53d8\u91cf\uff0c\u56e0\u6b64\uff1a
F² = (-\u221e\uff0c+\u221e)\u222be^(-2x²)dx * (-\u221e\uff0c+\u221e)\u222be^(-2y²)dy
= [D]\u222b\u222be^(-2x²)*dx * e^(-2y²)*dy
= [D]\u222b\u222be^[-2(x²+y²)]*dx *dy
\u5f0f\u4e2d\u79ef\u5206\u57dfD = {(x,y)|x \u2208(-\u221e\uff0c+\u221e),y\u2208(-\u221e\uff0c+\u221e)}
\u5bf9x\uff0cy\u8fdb\u884c\u6781\u5750\u6807\u53d8\u6362\uff0c\u5219:
x²+y² = \u03c1²\uff1bdxdy = \u03c1*d\u03c1*d\u03b8
F² = [D]\u222b\u222be^[-2(x²+y²)]*dx *dy
= [0,+\u221e)[0,2\u03c0]\u222b\u222be^(-2\u03c1²) \u03c1*d\u03c1*d\u03b8
= [0,2\u03c0]\u222bd\u03b8 *(0,+\u221e)\u222be^(-2\u03c1²) \u03c1*d\u03c1
= 2\u03c0* 1/4*[0,+\u221e)*\u222be^(-2\u03c1²) *d(2\u03c1²)
= \u03c0/2
\u56e0\u6b64 F = (-\u221e\uff0c+\u221e)\u222be^(-2x²)dx = \u221a(\u03c0/2) = (-\u221e\uff0c+\u221e)\u222be^(-2y²)dy
\u6240\u4ee5\u7b54\u6848\u4e3a(-1/2)\u221a(\u03c0/2) + (-1/2)\u221a(\u03c0/2)=-\u221a(\u03c0/2)
\u8be6\u7ec6\u8fc7\u7a0b\u5982\u56fert\u2026\u2026\u5e0c\u671b\u8fd9\u6837\u5199\u80fd\u591f\u6e05\u695a\u660e\u767d
50
lim(n->∞ ) n.[√(n^2-100) -n ]
=lim(n->∞ ) n.[(n^2-100) -n^2 ] /[√(n^2-100) +n ]
=lim(n->∞ ) -100n /[√(n^2-100) +n ]
=lim(n->∞ ) -100 /[√(1- 100/n^2) +1/n ]
=-100/(1+0)
=-100
绛旓細50
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