求极限的题X→1时求(1-X∧1/2)(1-X∧1/3).(1-X∧1/N)/(1-X)∧(N-1)
来源:学生作业帮 编辑:搜狗做题网作业帮 分类:数学作业 时间:2024/08/05 08:05:09
求极限的题X→1时求(1-X∧1/2)(1-X∧1/3).(1-X∧1/N)/(1-X)∧(N-1)
要详细解答,非常感谢
要详细解答,非常感谢
![求极限的题X→1时求(1-X∧1/2)(1-X∧1/3).(1-X∧1/N)/(1-X)∧(N-1)](/uploads/image/z/18410851-19-1.jpg?t=%E6%B1%82%E6%9E%81%E9%99%90%E7%9A%84%E9%A2%98X%E2%86%921%E6%97%B6%E6%B1%82%EF%BC%881-X%E2%88%A71%2F2%29%EF%BC%881-X%E2%88%A71%2F3%EF%BC%89.%EF%BC%881-X%E2%88%A71%2FN%EF%BC%89%2F%EF%BC%881-X%EF%BC%89%E2%88%A7%EF%BC%88N-1%EF%BC%89)
lim(1-X∧1/2)(1-X∧1/3).(1-X∧1/N)/(1-X)∧(N-1)=
lim[(1-X∧1/2)/(1-X)][(1-X∧1/3)/(1-X)].[(1-X∧1/N)/(1-X)]=
lim (1-X∧1/2)/(1-X)lim(1-X∧1/3)/(1-X)...lim(1-X∧1/N)/(1-X)
对每一个极限由洛必达法则可得lim(1-X∧1/K)/(1-X)=lim X^[(1/K)-1]/K=1/K
及得答案为(1/2) *(1/3)...(1/N)=1/N!
lim[(1-X∧1/2)/(1-X)][(1-X∧1/3)/(1-X)].[(1-X∧1/N)/(1-X)]=
lim (1-X∧1/2)/(1-X)lim(1-X∧1/3)/(1-X)...lim(1-X∧1/N)/(1-X)
对每一个极限由洛必达法则可得lim(1-X∧1/K)/(1-X)=lim X^[(1/K)-1]/K=1/K
及得答案为(1/2) *(1/3)...(1/N)=1/N!
求极限lim(x→∞)(1/n+2/n+3/n..+n/n)
求极限当x→0时,[N√(1+x)-1]/x/n.当x→-8时 [√(1-x)-3]/(2+3√x)
求极限x趋向无穷大时(1+x\n+x^2\2n^2)-n次方
求极限lim [x^(n+1)-(n+1)x+n]/(x-1)^2 x趋于1
求极限lim(x→1) (x⌒n -1)/(x-1)=?
当x→1时求lim(x∧3+2x)/(x-1)∧2的极限
求极限 ①lim x→n- (x-[x]) ②lim x→e log(x-1)/x-e ③limx→0+ log x^x
大一 微积分 求极限lim x→∞ (x+1)(x^2+1)……(x^n+1)/[(nx)^n+1]^[(n+1)/2]
求极限 lim(n→∞)[(1+x)/(1+x^2n)] |x|>1
求x趋于1,lim(x+x^2+……+x^n-n)/(x-1)的极限,
求极限:lim(n→∞)(x+1)(x-2)/(2x+1)(x-1)
求极限lim (n→+∞)ln(1+x^2)/ln(1+x^4)