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Assignment:Find the solution set of inequality e^(x+lnx) ≥x+lnx+1 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
e ^ ( x + ln x ) ≥ x + ln x + 1 (1)
From the definition field of ln
x > 0 (2 )
From the definition field of ln
x > 0 (3 )
From inequality(1):
x ≤ 567143/1000000 或 567143/1000000 ≤ x ≤ 567143/1000000 或 x ≥ 567143/1000000
From inequality(2):
x > 0
From inequality(3):
x > 0
From inequalities (1) and (2)
0 < x ≤ 567143/1000000 或 567143/1000000 ≤ x ≤ 567143/1000000 或 x ≥ 567143/1000000 (4)
From inequalities (3) and (4)
0 < x ≤ 567143/1000000 或 567143/1000000 ≤ x ≤ 567143/1000000 或 x ≥ 567143/1000000 (5)
The final solution set is :
0 < x ≤ 567143/1000000 或 567143/1000000 ≤ x ≤ 567143/1000000 或 x ≥ 567143/1000000Your problem has not been solved here? Please take a look at the hot problems !