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Assignment:Find the solution set of inequality abs(1/(sqrt((1-x^2)^2+(2*0.707*x)^2))-1) <0.01 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
abs ( 1 / ( sqrt ( ( 1 - x ^ 2 ) ^ 2 + ( 2 * 0.707 * x ) ^ 2 ) ) - 1 ) <0.01 (1)
From the definition field of √
( 1 - x ^ 2 ) ^ 2 + ( 2 * 0.707 * x ) ^ 2 ≥ 0 (2 )
From the definition field of divisor
sqrt ( ( 1 - x ^ 2 ) ^ 2 + ( 2 * 0.707 * x ) ^ 2 ) ≠ 0 (3 )
From inequality(1):
-0.377882 < x < 0.377882
From inequality(2):
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(3):
x ∈ R (R为全体实数),即在实数范围内,不等式恒成立!
From inequalities (1) and (2)
-0.377882 < x < 0.377882 (4)
From inequalities (3) and (4)
-0.377882 < x < 0.377882 (5)
The final solution set is :
-0.377882 < x < 0.377882 Your problem has not been solved here? Please take a look at the hot problems !