Proof of higher number function It is proved that the function y = xcosx is unbounded in (0, + infinity), but when x tends to infinity, this function is not infinite

Proof of higher number function It is proved that the function y = xcosx is unbounded in (0, + infinity), but when x tends to infinity, this function is not infinite

Proof: take a point column, xn = 2npaiyn = 2npai, then when n - > + 00, yn - > + 00, so y = xcosx has a point column that tends to be positive infinity at (0, + infinity), so this function is unbounded. To show that it is not infinite, take another point column, x'n = Pai / 2 + 2npai, then y'n = 0, and a point column tends to 0, that is, no matter whether x gets

Higher number proof function F (x) ∈ C [a, b], derivable in (a, b), a > 0. F (a) = 0 It is proved that there is a point in (a, b) ζ, Make f（ ζ）＝ （b- ζ） f＇（ ζ）/ a

Let f (x) = (b-X) ^ AF (x), f (a) = f (b) = 0, Rolle mean value theorem, there is C located in (a, b), so that f '(c) = 0, that is, f' (c) (B-C) ^ A-A (B-C) ^ (A-1) f (c) = 0, eliminate (B-C) ^ (A-1)

Find the definition field of the following function 1. Y = 1 / SiNx 2, y = LG (SiNx + 1) Find the domain of the following functions 1. y=1/sinx 2, y=lg(sinx+1) Great gods, solve

1: X is not equal to K π;
2: X is not equal to - π / 2 + 2K π (K ∈ z)

Find the definition field of 1 / 2 + SiNx under the function y = root

sinx+1/2>=0
sinx>=-1/2
Solution
2kπ-π/6

Find the definition field of function y = √ 1 / 2 + SiNx

1/2+sinx>=0
sinx>=-1/2
2kπ-π/6

Function y= The domain of X-1 + ln (2-x) is __

To make a function meaningful, you must meet
x-1≥0
2-x＞0 ， The solution is 1 ≤ x < 2,
‡ function y=
The domain of X-1 + ln (2-x) is [1,2),
So the answer is: [1, 2)