Given any positive real number, an algorithm is designed to find the area of the circle with this number as radius
The algorithm is as follows: Step 1: input a positive real number; step 2: calculate s = π R2; step 3: output s
If for all real numbers x, inequality
1. If the inequality (x ^ 4 + 2x ^ 2 + 4) / M (x ^ 2 + 2) ≥ 1 holds for all real numbers x, find the value range of M
1. If the inequality (x ^ 4 + 2x ^ 2 + 4) / M (x ^ 2 + 2) ≥ 1 holds for all real numbers x, find the value range of M
x^4+2x^2+4=(x^2+1)^2+3>0,x^2+2>0
So first confirm that M > 0
(x^4+2x^2+4)/m(x^2+2)≥ 1
(x^2+1)^2+3≥m(x^2+1)+m
(x ^ 2 + 1) ^ 2-m (x ^ 2 + 1) + 3-m ≥ 0, formula
(x^2+1 -m/2)^2 -(m^2)/4 +3-m≥0
For all real numbers x, the inequality holds
Then - (m ^ 2) / 4 + 3-m ≥ 0
m^2+4m-12≤0
(m+2)^2≤16
-6≤m≤2
To sum up, 0
If the opposite of a number is a non positive number, then the number must be ()
A. Negative B. positive C. 0 or positive D. 0
If the opposite number of a number is not positive, then the number must be 0 or positive, so choose C
If the opposite of a number is nonnegative, then the number must be negative
Let this number be X
Then - x ≥ 0
∴x≤0
The number must be non positive