*LG8 how to calculate the formula of such multiplication?

*LG8 how to calculate the formula of such multiplication?

lg5 *lg8
=lg5*lg2^3
=lg5*3lg2
=3lg5*lg2

Prove that x ^ x is an integrable function

How can it be a non - integral function? It's just that we can't get the form of the original function
X ^ x itself is a continuous function and must be integrable on a closed interval
The integrability of a function depends on whether the difference between the sum of Darboux upper and lower Darboux of different partitions in the same interval can be less than any positive number, which has nothing to do with whether to write its integral form
It is suggested that LZ self-study mathematical analysis

What kind of function is not integrable

Three types of integrable functions: 1. Continuous functions on closed intervals
2. Only a finite number of discontinuous points of the first kind are integrable, that is, piecewise continuous functions are integrable
3. Monotone bounded function must be integrable
This integrable type is called Riemann integrable. With the development of mathematical analysis, these integrable conditions are still too strong. Lebesgue integral appears, and the conditions of integrable function are more relaxed. If you are interested, you can go to see books on numerical analysis

Do you need to find the domain to find the derivative function? I mean, when doing the paper, why not write it and give it to the teacher? Besides, the teacher is not strict

If necessary, for example, f (x) = lgx, and its derivative f '(x) = 1 / X
From F (x) = lgx, the definition field is (0, + infinity)
Therefore, the derivative function f '(x) = 1 / X must be greater than 0, that is, the original function increases monotonically in the definition domain

Why does a function appear in the derivation of a function Does the derivative function mean that the connecting line of each tangent point on the original function is called the derivative function?

The derivative function is a function composed of the tangent of each tangent point on the original function and the slope of the tangent

Two high school function questions 3. If the maximum and minimum values of y = a-bsin (4x - π / 3) are 5 and 1 respectively, then a=____ b=_____ 4. F (x) = SiNx + 1 / SiNx, X belongs to (0, π), then the minimum value of F (x) is____ Can I have the last two more? It's very simple. 1. Find y = cos ² Value range of X + SiNx + 1 (|x| ≤ 1) 2. Find the function y = sin ² Maximum and minimum values of X-5 / 2sinx + 5 / 2

Well, I calculated for you. In question 3, a = 3, B = 2 or B = - 2. In question 4, f (x) min = 2. For question 3, the simple analysis is as follows: a + | B | = 5, a - | B | = 1, so the joint solution is a = 3, B = 2 or - 2. As for question 4, we can regard this function as the form of F (x) = x + 1 / X. in this form, X belongs to (0,1). Therefore, f (x) min = 2. I hope your grades are better and better and realize your dream!