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☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality 10 >1.5*0.5/1.4*x*(1/(1-e^(-0.1*x))*e^(-0.1*x)-1/(1-e^(-1.5*x))*e^(-1.5*x)) >3 .
Question type: Inequality
Solution:
The inequality can be reduced to 2 inequalities:
10 >1.5 * 0.5 / 1.4 * x * ( 1 / ( 1 - e ^ ( -0.1 * x ) ) * e ^ ( -0.1 * x ) - 1 / ( 1 - e ^ ( -1.5 * x ) ) * e ^ ( -1.5 * x ) ) (1)
1.5 * 0.5 / 1.4 * x * ( 1 / ( 1 - e ^ ( -0.1 * x ) ) * e ^ ( -0.1 * x ) - 1 / ( 1 - e ^ ( -1.5 * x ) ) * e ^ ( -1.5 * x ) ) >3 (2)
From the definition field of divisor
1 - e ^ ( -0.1 * x ) ≠ 0 (3 )
From the definition field of divisor
1 - e ^ ( -1.5 * x ) ≠ 0 (4 )
From inequality(1):
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(2):
-√397610951/√3500000 < x < √397610951/√3500000
From inequality(3):
x < 0 或 x > 0
From inequality(4):
x < 0 或 x > 0
From inequalities (1) and (2)
-√397610951/√3500000 < x < √397610951/√3500000 (5)
From inequalities (3) and (5)
-√397610951/√3500000 < x < 0 或 0 < x < √397610951/√3500000 (6)
From inequalities (4) and (6)
-√397610951/√3500000 < x < 0 或 0 < x < √397610951/√3500000 (7)
The final solution set is :
-√397610951/√3500000 < x < 0 或 0 < x < √397610951/√3500000 Your problem has not been solved here? Please take a look at the hot problems !