Given that the periodic function f (x) is an odd function with a period of 4 and f (- 1) = 1, find the value of F (- 3)

Given that the periodic function f (x) is an odd function with a period of 4 and f (- 1) = 1, find the value of F (- 3)

Because f (x) = f (x + 4), - f (x) = f (- x), f (- 3) = f (- 3 + 4) = f (1) = - f (- 1) = - 1

Let f (x) (x ∈ R) be an odd function. F (1) = - 1 / 2 and f (x + 2) = f (x) + 2, find the value of F (3)

Let x = 1. Then f (3) = f (1) + 2 = - 1 / 2 + 2 = 3 / 2

Let f (x) = AX2 + 1 / BX = C be an odd function (a, B, C are integers), and f (1) = 2, f (2)

Let f (x) = BX + C / AX2 + 1 (a, B, C belong to Z) be an odd function if f (1) = 2,2

f(x)=(ax²+1)/(bx+c)
∵ f (x) is an odd function ∵ C = 0
And f (1) = (a + 1) / b = 2
∴a+1=2b
∵f(2)=(4a+1)/(2b)

Given that the real number a, B, C is an equal ratio sequence, and the projection of point P (1,0) on the straight line ax + by + C = 0 is Q, then what is the equation of Q? X ^ 2 + (y + 1) ^ 2 = 2
Given that the real number a, B, C is an equal ratio sequence and the projection of point P (1,0) on the straight line ax + by + C = 0 is Q, then what is the equation of Q?
x^2+(y+1)^2=2

b²=ac
Ax + by + C = 0, the slope is - A / b
The slope of the vertical line is B / A
So the straight line is y-0 = B / A * (x-1), y = B (x-1) / A
The coordinate of the intersection point with the original line is the Q equation
By introducing the original equation, x = (B & sup2; - AC) / (A & sup2; + B & sup2;)
y=-b(a+c)/(a²+b²)
If the ratio x is zero, it's not realistic

In rectangular paper ABCD, ab = 3cm, BC = 4cm. Now fold and flatten the paper so that a and C coincide. If the crease is EF, the area of the overlapping part △ AEF is equal to______ ．

Let AE = x, from the folding, EC = x, be = 4-x, in RT △ Abe, AB2 + be2 = AE2, that is 32 + (4-x) 2 = X2, the solution is: x = 258, from the folding, we can know ∠ AEF = ∠ CEF, ∵ ad ‖ BC, ∵ CEF = ∠ AFE, ∵ AEF = ∠ AFE, that is AE = AF = 258, ∵ s △ AEF = 12 × AF × AB = 12 × 258 × 3 = 7516

Given function y = √ (1 / a) x + 1 (a)

By making the function y = √ (1 / a) x + 1 meaningful in the domain of definition, X / A + 1 > = 0, x = 1, a

1×2×3×4.×200=?

This problem is not likely to be a Mathematical Olympiad problem: the result is a factorial of 200, which can be calculated by Stirling's formula (because it should be superordinated) 200! = 78865786736479050355236321393218506229513597768717326329474253324435944996340334292030428401198462390417721

Factoring factor 3x ^ 2-3x-1 in the range of real numbers

First, the root is x = (3 ± √ 21) / 6
So the factorization is [x - (3 + √ 21) / 6] [x - (3 - √ 21) / 6] = 0

In the cube abcd-a1b1c1d1 with edge length a, the edge length is a, and the cosine value of the angle between BB1 and section ab1c is calculated
Find the distance from point B to section ab1c

Ab1c is an equilateral triangle, and then it is easy to know that the projection of B is actually the three center points (center of gravity, centroid) of the triangle, so the common method is to draw an equilateral triangle, and find out the distance from the center of gravity to the vertex to solve this problem. But there are many ideas in solid geometry. For example, we can use the equal volume method. It is easy to know that the volume of the tetrahedron is SH / 3, So we can use two angles to calculate the volume. One angle is to select the bottom surface on the surface of the cube. At this time, the area and height of the bottom are known. We can calculate the volume, then transform the bottom surface, and take △ ab1c as the bottom surface. Then the distance from point B to section ab1c is the corresponding height. We can solve the problem by listing the equation