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Assignment:Find the solution set of inequality x(ln(1+x)-ln(1-x)) ≥1+cosx+(1/2)x^2 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
x * ( ln ( 1 + x ) - ln ( 1 - x ) ) ≥1 + cos x + ( 1 / 2 ) * x ^ 2 (1)
From the definition field of ln
1 + x > 0 (2 )
From the definition field of ln
1 - x > 0 (3 )
From inequality(1):
x ≤ -0.836069 或 x ≥ 0.836069
From inequality(2):
x > -1
From inequality(3):
x < 1
From inequalities (1) and (2)
-1 < x ≤ -0.836069 或 x ≥ 0.836069 (4)
From inequalities (3) and (4)
-1 < x ≤ -0.836069 或 0.836069 ≤ x < 1 (5)
The final solution set is :
-1 < x ≤ -0.836069 或 0.836069 ≤ x < 1Your problem has not been solved here? Please take a look at the hot problems !