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☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality 0
Question type: Inequality
Solution:
The inequality can be reduced to 8 inequalities:
0 < sin x (1)
sin x < cos x (2)
cos x < lg x (3)
lg x < ln x (4)
From the definition field of lg
x > 0 (5 )
ln x < x (6)
From the definition field of ln
x > 0 (7 )
x < x ^ 2 (8)
x ^ 2 < e x (9)
e x <10 ^ x (10)
From inequality(1):
x < -15.707963 或 -12.566371 < x < -9.424778 或 -6.283185 < x < -3.141593 或 0 < x < 3.141593 或 6.283185 < x < 9.424778 或 x > 12.566371
From inequality(2):
-14.922565 < x < -11.780972 或 -8.63938 < x < -5.497787 或 -2.356194 < x < 0.785398 或 3.926991 < x < 7.068583 或 10.210176 < x < 13.351769
From inequality(3):
1.418406 < x < 5.552112 或 x > 6.863082
From inequality(4):
x > 1
From inequality(5):
x > 0
From inequality(6):
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(7):
x > 0
From inequality(8):
x < 0 或 x > 1
From inequality(9):
x > -0.703467
From inequality(10):
x > 0
From inequalities (1) and (2)
-12.566371 < x < -11.780972 或 -6.283185 < x < -5.497787 或 0 < x < 0.785398 或 6.283185 < x < 7.068583 或 12.566371 < x < 13.351769 (11)
From inequalities (3) and (11)
或 或 -12.566371 < x < -11.780972 或 6.863082 < x < 7.068583 或 12.566371 < x < 13.351769 (12)
From inequalities (4) and (12)
6.863082 < x < 7.068583 或 12.566371 < x < 13.351769 (13)
From inequalities (5) and (13)
6.863082 < x < 7.068583 或 12.566371 < x < 13.351769 (14)
From inequalities (6) and (14)
6.863082 < x < 7.068583 或 12.566371 < x < 13.351769 (15)
From inequalities (7) and (15)
6.863082 < x < 7.068583 或 12.566371 < x < 13.351769 (16)
From inequalities (8) and (16)
6.863082 < x < 7.068583 或 12.566371 < x < 13.351769 (17)
From inequalities (9) and (17)
6.863082 < x < 7.068583 或 12.566371 < x < 13.351769 (18)
From inequalities (10) and (18)
6.863082 < x < 7.068583 或 12.566371 < x < 13.351769 (19)
The final solution set is :
6.863082 < x < 7.068583 或 12.566371 < x < 13.351769 Your problem has not been solved here? Please take a look at the hot problems !