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☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality (e^(-0.5*x^(1/4)))/((1+x^(1/8))sqrt(3.14)) <= lnx/sqrt(x) .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
( e ^ ( -0.5 * x ^ ( 1 / 4 ) ) ) / ( ( 1 + x ^ ( 1 / 8 ) ) * sqrt ( 3.14 ) ) <= ln x / sqrt ( x ) (1)
From the definition field of divisor
( 1 + x ^ ( 1 / 8 ) ) * sqrt ( 3.14 ) ≠ 0 (2 )
From the definition field of ln
x > 0 (3 )
From the definition field of √
x ≥ 0 (4 )
From inequality(1):
x ≥ 2.256796
From inequality(2):
x ∈ R (R为全体实数),即在实数范围内,不等式恒成立!
From inequality(3):
x > 0
From inequality(4):
x ≥ 0
From inequalities (1) and (2)
x ≥ 2.256796 (5)
From inequalities (3) and (5)
x ≥ 2.256796 (6)
From inequalities (4) and (6)
x ≥ 2.256796 (7)
The final solution set is :
x ≥ 2.256796Your problem has not been solved here? Please take a look at the hot problems !