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☆1 inequalities
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Assignment:Find the solution set of inequality lg((tanx:sqrt(x+x^0))+1)/x <0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
lg ( ( tan x : sqrt ( x + x ^ 0 ) ) + 1 ) / x <0 (1)
From the definition field of √
x + x ^ 0 ≥ 0 (2 )
From the definition field of lg
( tan x : sqrt ( x + x ^ 0 ) ) + 1 > 0 (3 )
From the definition field of divisor
x ≠ 0 (4 )
From inequality(1):
x < 3.141593
From inequality(2):
x ≥ -1
From inequality(3):
x < -1 或 -0.57677 < x < 1.570796 或 2.088148 < x < 4.712389 或 5.097183 < x < 7.853982 或 8.172889 < x < 10.995574 或 x > 11.27362
From inequality(4):
x < 0 或 x > 0
From inequalities (1) and (2)
-1 ≤ x < 3.141593 (5)
From inequalities (3) and (5)
-0.57677 < x < 1.570796 或 2.088148 < x < 3.141593 (6)
From inequalities (4) and (6)
-0.57677 < x < 0 或 0 < x < 1.570796 或 2.088148 < x < 3.141593 (7)
The final solution set is :
-0.57677 < x < 0 或 0 < x < 1.570796 或 2.088148 < x < 3.141593 Your problem has not been solved here? Please take a look at the hot problems !