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From known, f(-x)=f(x) , and f(-x-1)=-f(x-1) , so f(x)=f(-x)=f[-(x-1)-1]=-f[(x-1)-1]=-f(x-2) , so f(x+2)=-f[(x+2)-2]=-f(x) , so f(x+4)=f[(x+2)+2]=-f(x+2)=f(x) , Then f( .
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f(x-1) is an odd function, then let: g(x)=f(x-1)g(-x)=-g(x) i.e.: f[(-x)-1]=-f(x-1)f(-x-1)=-f(x-1).2
and f(x) is an even function:
f(x)=f(-x) Replace x with x+1
f(x+1)=f(-x-1) is substituted into 2.
f(x+1)=-f(x-1)
Let x+1=t x=t-1
f(t)=-f(t-1-1)=-f(t-2)f(x)=-f(x-2)f(
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f(x) is an even function with respect to y-week symmetry, and a translation of 1 unit to the right f(x —1) is an odd function, and you can exit f(x) with respect to x=2 symmetry. The period t=2(2—0), so the period of f(x) is 4, and f(abstraction into a trigonometric function is simple.)
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Solution: cota=cosa sina = -12 5, sina = -5 12cosa, from cosa 2 + sina 2=1, get 169 144cosa 2=1, get cosa = 12 13, cot = 1 tan <0, in the triangle abc each angle is not more than 180 degrees, it can be seen that the angle a is an obtuse angle, then cosa = -12 13
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In this problem, given the value of a trigonometric function of a certain angle, the value of other trigonometric functions is found by hiding the condition given a defined domain. cota=, then a is an obtuse angle. COSA is negative. From the relationship between trigonometric functions, cosa = -12 13
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By cota is negative, a is an obtuse angle, put the complementary angle d of a into a triangle of straight angles dbc, b is a right angle, let db be 12x, then bc is 5x, by the pythagorean theorem, dc is 13x, cosd is 12 13, d is the complementary angle of a, then cota is -12 13
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The low radius of the cylinder is 5 for the busbar and the shortest is half a cylinder (I don't know?). ) is as short as [52+(.]
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The straight line between two points is the shortest. Place the sides of the cylinder, getting.
l=√[5²+(5π/2)²]
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Put the side, easy to know, for ((approx. equal to.)
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Rationale: This set is actually made up of four elements: i, -i, -1, and 1
Choose two out of four, there are 6 possibilities, and there are only 2 with a sum of 0. So the probability is 1 3
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That is, in the set [1,-1,i,-i], you can repeatedly select 2 numbers, and there are 4 combinations of 0 and 0, that is, the second number is selected to correspond to the first number.
The total combination is 4*4=16
Then the probability is 4 16 = 25%.
Known -1a-b>2....4)
Anisotropic inequalities can be subtracted, and the direction of the unequal sign after subtraction is the same as the direction of the inequality sign of the subtracted formula, therefore: >>>More
1. Let the residual amount be y, then, y=10t - 24 (5t) +100[ 10t)] 2 - 2* 10t) *6 2) +6 2) 2 -(6 2) 2 +100 >>>More
1.Because a=1, c=0, so f(x)=x 2+bx 1, that is, f(x)-1 0, that is, x 2+bx-1 0, and then the main dimension is reversed, and b is regarded as the main element, and x is regarded as the dimension, that is, x is known, so it becomes a one-dimensional inequality about b, because x (0, 1, so the inequality is brought in, -1 0 is constant, 1 2+1 b-1 0, and b 0, in summary, b 0 2That is, 4 x + m (2 x) + 1 = 0 holds, and the equal sign shifts both sides, that is, m=-(2 x+2 -x), that is, find the range of f(x) = -(2 x+2 -x), because x r, so (2 x) (0, + commutation, so that 2 x=t, t (0, + i.e., the original formula is y=-(t+1 t), and y (-2) is obtained from t, that is, m (-2).
Solution: The sum of the first n terms of the sequence is sn=2n2 >>>More
f(0+0)=f(0)+f(0)
f(0)=2f(0) >>>More