The proof that ∫ (0, x) f (T) DT - ∫ (- x, 0) f (T) DT is a periodic function F (x) is a continuous function with period T on R. it is proved that ∫ (0, x) f (T) DT - ∫ (- x, 0) f (T) DT is also a function with period T

The proof that ∫ (0, x) f (T) DT - ∫ (- x, 0) f (T) DT is a periodic function F (x) is a continuous function with period T on R. it is proved that ∫ (0, x) f (T) DT - ∫ (- x, 0) f (T) DT is also a function with period T

Let f (x + T) be f (x + T) = 8747; (0, x) f (T) f (T) f (T) t (f (x + T) = 8747 (0, x + T) f (T) f (x (x + T) f (x + T) f (x + T) f (x + T) is f (x + T) = 8747 (0, X (0, x) f (T) f (x (x + T) f (T) f (f (x + T) is f (x + T) = (0 (0, X (0, x, x + T) f (T) f (t (t (T) f (f (x (x + T) f (x + T) f (x (x + T) f (x + T) f (x + T) f (x (x + T (x + T))) \\8747x) + ∫ (x, x + T)

If the function f (x) is differentiable in the interval [0, a], and f (a) = 0, it is proved that there is at least one point ξ in the interval (0, a), such that f (ξ) + ξ f ′ (ξ) = 0

Constructing a new function g (x) = XF (x)
Because g (0) = g (a) = 0
So there must be X
Let g '(x) = 0

Let f (x) be second-order differentiable in the interval [0,1], and f (0) = 0, f '' (x) > 0. It is proved that f (x) / X is a monotone increasing function in (0,1)

Because f '' (x) > 0
So f '(x) is an increasing function
If f (0) = 0, then f '(x) increases monotonically in (0,1] and f' (x) > 0
So the proposition is proved

A and B are moving in the same direction on the road at a constant speed. A's speed is 3 km / h, and B's speed is 5 km / h. A passes through place a at 12 noon, and B passes through place a at 2 pm. What time can b catch up with a in the afternoon? How far is it from ground a?

According to the meaning of the question: 6 + 3x = 5x, the solution is: x = 3, 5 × 3 = 15 (km). Answer: B can catch up with a at 5 p.m., and the distance to a is 15km

After three seventh of the fraction is converted into a decimal, what is the number on the 2011 digit after the decimal point? What is the sum of these 2011 digits

7 / 3 = 0.428571428571. Every six cycles, 2011 / 6 quotient 335 more than 1, so it should be the first number of the cycle 4, the sum of the numbers is (4 + 2 + 8 + 5 + 7 + 1) * 335 + 4 = 9049

A and B are going from A.D. to A.D. they meet at 4 o'clock. A travels 60 kilometers per hour and B 40 kilometers per hour. They meet at the midpoint. When does B go first

If a meets after walking for 4 hours, then:
A: 60 * 4 = 240 km
Meet at the midpoint
So B also walked 240 kilometers
So the total time is: 240 / 40 = 6 (hours)
So first 6-4 = 2 (hours)

On the square root and Pythagorean theorem!
1. If √ 1-m (m in the root sign) + 1 / M (1 / 2 of the root sign m) is meaningful, find the value range of M
2. In △ ABC, it is known that ab = 13cm, BC = 10cm, and the midline ad on the edge of BC = 12cm. Please compare the size of edge AB and edge AC
3. If the three sides of △ ABC are a, B, C, and a ^ 2 + B ^ 2 + C ^ 2 + 200 = 12a + 16b + 20c, try to judge the shape of △ ABC

1. The number in the root sign should be greater than or equal to 0, and the numerator cannot be 0
So 1-m > = 0 and M is greater than 0
That is 0

The two trains run 480 km apart, and the two trains meet four hours later. It is known that car a runs 55 km per hour and car B how many km per hour

Vehicle B speed = 480 △ 4-55 = 65 km / h

Given that the average of a, B, C, D and E is. X, then the average of a + 5, B + 12, C + 22, D + 9 and E + 2 is______ ．

The average of ∵ a, B, C, D and E is. X, ∵ a + B + C + D + e = 5. X, ∵ the average of a + 5, B + 12, C + 22, D + 9 and E + 2 is (a + 5 + B + 12 + C + 22 + D + 9 + e + 2) ∵ 5 = (a + B + C + D + e + 50) ∵ 5 = (5. X + 50) ∵ 5 =. X + 10

Party A and Party B are facing each other. Party A travels 18 kilometers per hour by bike, while Party B travels three times as much by motorcycle per hour as Party A. after three o'clock, they meet. How many kilometers is the distance between the two places

B: 18 × 3 = 54 km / h by motorcycle
So the distance between the two places is (18 + 54) × 3 = 216 km