解çï¼
å½n=1æ¶
z(x) = e^(x-1) - x
z1(x) = e^(x-1) -1 ï¼ä¸ºz(x)çä¸é¶å¯¼æ°ï¼
å½xâï¼1ï¼+âï¼æ¶
z1(x) æéå¢ æ以z1(x)>z1(1)=0
æ以z(x)æéå¢
z(x)>z(1)=0
ä¹å°±æ¯e^(x-1)ï¼x^n/nï¼å¨n=1æ¶ç«
åå
e^(x-1)ï¼x^n/nï¼å¨n=kæ¶æç«
å³e^(x-1) > x^k/k!
e^(x-1) - x^k/k! >0
åå½n=k+1æ¶
z(x) = e^(x-1)-x^(k+1)/(k+1)ï¼
z1(x) = e^(x-1) - (k+1)x^k/(k+1)!
= e^(x-1) - x^k/k!>0
ç±ä¸ä¸æ¥n=kæ¶çç»è®º
å½xâï¼1ï¼+âï¼æ¶
z1(x)æ大äº0
æ以z(x)æéå¢
æ以z(x)>z(1)= 1 -1^(k+1)/(k+1)ï¼=1-1/(k+1)!>0
æ以e^(x-1)ï¼x^(k+1)/(k+1)ï¼
y=x-3aä¸y=-x+a-1
x-3a=-x+a-1
2x=4a-1
x=(4a-1)/2
y=x-3a=(4a-1)/2-3a=(-2a-1)/2
交ä¸ç¬¬ä¸è±¡éå:
(4a-1)/2ï¼0
aï¼1/4
(-2a-1)/2ï¼0
aï¼-1/2
â´-1/2ï¼aï¼1/4
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