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Assignment:Find the solution set of inequality 0 <(lnx)/(x^(0.5)) <0.000001 .
Question type: Inequality
Solution:
The inequality can be reduced to 2 inequalities:
0 < ( ln x ) / ( x ^ ( 0.5 ) ) (1)
( ln x ) / ( x ^ ( 0.5 ) ) <0.000001 (2)
From the definition field of ln
x > 0 (3 )
From the definition field of divisor
x ^ ( 0.5 ) ≠ 0 (4 )
From inequality(1):
x > 1
From inequality(2):
x < 1000001/1000000
From inequality(3):
x > 0
From inequality(4):
x ∈ R (R为全体实数),即在实数范围内,不等式恒成立!
From inequalities (1) and (2)
1 < x < 1000001/1000000 (5)
From inequalities (3) and (5)
1 < x < 1000001/1000000 (6)
From inequalities (4) and (6)
1 < x < 1000001/1000000 (7)
The final solution set is :
1 < x < 1000001/1000000 Your problem has not been solved here? Please take a look at the hot problems !