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Assignment:Find the solution set of inequality 1/x+√tan(asinx-2)-lg(ex-(x+e)^0) ) <10000 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
1 / x + √ tan ( arcsin x - 2 ) - lg ( e x - ( x + e ^ 0 ) ) <10000 (1)
From the definition field of divisor
x ≠ 0 (2 )
From the definition field of arcsin
x ≥ -1 (3 )
x ≤ 1 (4 )
From the definition field of lg
e x - ( x + e ^ 0 ) > 0 (5 )
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):
x < 0 或 x > 0
From inequality(3):
x ≥ -1
From inequality(4):
x ≤ 1
From inequality(5):
x < 0 或 x > 0
From inequalities (1) and (2)
x < 0 或 x > 0 (6)
From inequalities (3) and (6)
-1 ≤ x < 0 或 x > 0 (7)
From inequalities (4) and (7)
-1 ≤ x < 0 或 0 < x ≤ 1 (8)
From inequalities (5) and (8)
-1 ≤ x < 0 或 0 < x < 0 或 0 < x ≤ 1 (9)
The final solution set is :
-1 ≤ x < 0 或 0 < x < 0 或 0 < x ≤ 1 Your problem has not been solved here? Please take a look at the hot problems !