推 jacky7987 :第二個我會先想到用g_j(t)=(x_1,...,t,...,x_n) 09/10 23:53
→ jacky7987 :choose x=(x_1,...,x_n) 09/10 23:54
1.要如何證明 (1 + x/n)^n converges uniformly to e^x on any closed bounded
interval of |R as n →∞.
n m
2.Suppose that r > 0,that a€|R ,and that f:B(a,r)→|R .If all first-order
partial derivative of f exist on B(a,r) and satisfy
[每個分量的偏微分都等於零] fxj(x) = 0 for all x €B(a,r) and all j=1,2,...,n,
prove that f has only one value on B(a,r).
第一題不知道是不是只要找出｜(1 + x/n)^n - e^x｜的上界，然後在用極限去證明
不過還是不會寫XD
第二題很直覺 但是要寫正式的證明卻不知道該怎麼寫
希望版上得高手能給個指教
先說謝了～
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