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☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality ln(1+1/x)-1/1+x-1/√x(1+x) <0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
ln ( 1 + 1 / x ) - 1 / 1 + x - 1 / √ x * ( 1 + x ) <0 (1)
From the definition field of divisor
x ≠ 0 (2 )
From the definition field of ln
1 + 1 / x > 0 (3 )
From the definition field of √
x ≥ 0 (4 )
From inequality(1):
x < 3.02996
From inequality(2):
x < 0 或 x > 0
From inequality(3):
x < -1 或 x > 0
From inequality(4):
x ≥ 0
From inequalities (1) and (2)
x < 0 或 0 < x < 3.02996 (5)
From inequalities (3) and (5)
x < -1 或 0 < x < 3.02996 (6)
From inequalities (4) and (6)
0 < x < 3.02996 (7)
The final solution set is :
0 < x < 3.02996 Your problem has not been solved here? Please take a look at the hot problems !