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Assignment:Find the solution set of inequality lg(asinx)-sqrt(1/x)+(tanx)^0 >-5 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
lg ( arcsin x ) - sqrt ( 1 / x ) + ( tan x ) ^ 0 > -5 (1)
From the definition field of arcsin
x ≥ -1 (2 )
x ≤ 1 (3 )
From the definition field of lg
arcsin x > 0 (4 )
From the definition field of divisor
x ≠ 0 (5 )
From the definition field of √
1 / x ≥ 0 (6 )
From inequality(1):
x > 0.045994
From inequality(2):
x ≥ -1
From inequality(3):
x ≤ 1
From inequality(4):
x > 0
From inequality(5):
x < 0 或 x > 0
From inequality(6):
x ≥ 0
From inequalities (1) and (2)
x > 0.045994 (7)
From inequalities (3) and (7)
0.045994 < x ≤ 1 (8)
From inequalities (4) and (8)
0.045994 < x ≤ 1 (9)
From inequalities (5) and (9)
0.045994 < x ≤ 1 (10)
From inequalities (6) and (10)
0.045994 < x ≤ 1 (11)
The final solution set is :
0.045994 < x ≤ 1 Your problem has not been solved here? Please take a look at the hot problems !