Which formula of binomial theorem Give me the formula, as well as the meaning and calculation format of each item

Which formula of binomial theorem Give me the formula, as well as the meaning and calculation format of each item

Proving by binomial theorem
(1) 63 ^ 63 + 17 can be divided by 16
(2) 3 ^ 4N + 2 + 5 ^ 2n + 1 can be divided by 14

It is proved by binomial theorem that (1) 63 ^ 63 + 17 can be divided by 16. 63 ^ 63 + 17 = (16 * 4-1) ^ 63 + 17 is expanded by binomial theorem = (16 * 4) ^ 63 + C (1,63) * (16 * 4) ^ 62 * (- 1) ^ 1 + C (2,63) * (16 * 4) ^ 61 * (- 1) ^ 2 + C (3,63) * (16 * 4) ^ 61 * (- 1) ^ 2 +... + C (63,63) * (- 1) ^ 63 + 17

Given the function f (x) = 1 / x + alnx (a is not equal to 0, a is a real number), if there is at least one point XO in the interval [1, e], then f (XO)

If a > 0, f (x) maximum f (E) = 1 / x + a

It is known that a and B are opposite to each other, and neither of them is 0. C and D are reciprocal to each other. The absolute value of X is 5
Find 2a of 2010 (a + b) + CDX + B
I don't know how to score, so I have to make it like this, ha ha!

a. B is opposite to each other, a + B = 0, a / b = - 1
c. D reciprocal CD = 1
The absolute value of X is 5, x = plus or minus 5
So 2010 (a + b) + CDX + 2A / b
=2010*0+1*x+2*-1
=x-2
When x = 5, the original formula is 3
When x = - 5, the original formula = - 7

Comparison of logarithm function bases
In the same rectangular coordinate system, there are many images of different logarithmic functions. How do you compare the size of their bases

If several logarithmic functions with different bases are placed in the same plane rectangular coordinate system, the higher the base number is, the closer the upper part of the x-axis of the image is to the right
For example, the image of y = loga (x) is closer to the right than the image of y = logb (x)

The vector a = (- 1,2) and the vector b = (1,1) t ∈ R are known. ① find the cosine value of the angle between the vector a and the vector B; ② find the minimum value of a + TB and the corresponding t value

(1) Vector A. vector b = (- 1) * 1 + 2 * 1 = 1. | a | = √ 5, | B | = √ 2. Cos = A.B / | a | B |. = 1 / (√ 5 * √ 2).. cos = √ 10 / 10. --- cosine value of the angle between vector a and vector B. (2). Vector (a + TB) = (- 1 + t.2 + T). | a + TB | = √ [(- 1 + T) ^ 2 + (2 + T) ^ 2]. = √ (2t ^ 2 + 2T + 5) = [2 (T + 1 / 2

The definition field of function f (x) = LG √ (3-2x) is?

The logarithm function requires that the base is greater than 0 and not equal to 1, and the logarithm is greater than 0. So 3-2x > 0, so X

Given that the function f (x) = ax + B1 + X2 is an odd function defined on (- 1,1), and f (12) = 25, find the analytic expression of function f (x)

∵ f (x) is an odd function defined on (- 1,1). ∵ f (0) = 0, that is, a × 0 + B1 + 02 = 0, ∵ B = 0, f (12) = 12a1 + (12) 2 = 25, ∵ a = 1, ∵ f (x) = X1 + x2

Given that f (x) = a 2x + A-2 / 2x + 1, the function f (x) = a * 2x + A-2 / 2x + 1 whose domain is r satisfies f (- x) = - f (x), the value of a is determined, and it is proved that f (x) is in R

(1) ∵ f (x) = (A2 ^ x + A-2) / (2 ^ x + 1) ∵ f (- x) = (A2 ^ x + A-2) / (2 ^ x + 1) - f (x) = - (A2 ^ x + A-2) / (2 ^ x + 1) from F (- x) = - f (x), the solution is a = 2 (2) ∵ f (x) = 2 * 2 ^ X / (2 ^ x + 1) ∵ f (x) = 2 + 2 / (2 ^ x + 1) ∵ 2 ^ x + 1 monotone increasing ∵ f (x) monotone decreasing

If a and B represent rational numbers, and the value of a + B is greater than that of A-B, then ()
A. A, B are the same, B. A, B are different, C. A > 0d. B > 0

Because a + B ＞ A-B, then B ＞ - B, so 2B ＞ 0, B ＞ 0