On the concept of function continuity and the problem of limit F (x) = a (x = 1) f (x) = x ^ 3-1 / X-1, (x is not equal to 1) If f (x) is continuous on R, then a is equal to () LIM (an-1 / N + 2A / 3n)= n→∞ robin_ two thousand and six LIM (x → 1) (x ^ 3-1) / (x-1) how to deduce LIM (x → 1) (x ^ 2 + X + 1)

On the concept of function continuity and the problem of limit F (x) = a (x = 1) f (x) = x ^ 3-1 / X-1, (x is not equal to 1) If f (x) is continuous on R, then a is equal to () LIM (an-1 / N + 2A / 3n)= n→∞ robin_ two thousand and six LIM (x → 1) (x ^ 3-1) / (x-1) how to deduce LIM (x → 1) (x ^ 2 + X + 1)

F (1) = Alim (x → 1) f (x) = LIM (x → 1) (x ^ 3-1) / (x-1) = LIM (x → 1) (x ^ 2 + X + 1) = 3. Therefore, when a = 3, f (x) is continuous at x = 1, so it is continuous at R

How can a function find a formula from a vertex?
Question: vertex - 1, greater than another two points, less than - 1,0 less than 1,0 find b > 0 a + B + C0 4a-2b + C1 which three are right

It is not enough to determine one vertex of a function
At least another point on the function

A problem about function limit -- break point
The function f (x) = x, 0 ≤ x < 1, f (x) = 0, x = 1, the discontinuity is x = 1, why is it a removable discontinuity?

As long as f (1) = 1, the discontinuity can be removed, so it is a removable discontinuity

f(x+2)=[1+f(x)]/[1-f(x)] (x∈R)
1. Prove that f (x) is a periodic function
2. If f (3) = - 3, find the value of F (2003)
You seem to be wrong? It should be f (x + 2) = - 1 / F (X-2)

From the expression, we know that f (x) = [1 + F (X-2)] / [1-f (X-2)], substitute f (x + 2) = - 1 / F (X-2), f (X-2) = - 1 / F (X-6), f (x + 2) = f (X-6), so it is a periodic function with 8 as the period. F (2003) = f (250 * 8 + 3) = f (3) = - 3

How to find the period of periodic function
If the minimum positive period of function y = cos (KX / 4 + π / 3) (k > 0) is not greater than 2, then the minimum value of positive integer k should be ()
（A）10
（B）11
（C）12
（D）13

T=2π/(K/4)=8π/K==4π=12.56
K=13
Choose D

The title of periodic function
It is known whether the function f (x) defined on the set of real numbers always satisfies the condition that f (x + 2) = - f (x) is a periodic function. If it is a periodic function, its period is obtained

f(x+2)=-f(x)
f(x+4)=-f(x+2)
f(x+2)=-f(x)
f(x)=f(x+4)
Is a periodic function, period 4

The properties of periodic function
The definition field of function f (x) is a real number, which is an odd function, and f (x + 2) = - f (x). When x is greater than or equal to - 1 and less than or equal to 1, f (x) = the cube of X. find the analytic expression of function when x is greater than or equal to 1 and less than or equal to 5

From F (x + 4) = - f (x + 2) = f (x), the period is 4
When 3 ≤ x ≤ 5, - 1 ≤ x-4 ≤ 1 f (x) = f (x-4) = (x-4) ^ 3
When 1 ≤ x

F (x) is a function defined on R, and for any x belonging to R, it satisfies: B [f (x + P) + F (x)] = a [1-f (x) + F (x + P)], where a, B and P are non-zero constants. Proof: f (x) is a periodic function

B[F(X+P)+F(X)]=A[1-F(X)+F(X+P)]
F(X+P)=[(A+B)/(A-B)]F(X)-A/(A-B)
A. B and P are nonzero constants
That is, f (x + P) = MF (x) - n
According to theorem 1
If f (x) is a periodic function with t as the minimum positive period on set M, then KF (x) + C (K ≠ 0) and 1 / F (x) are periodic functions with t as the minimum positive period on set M and set {X / F (x) ≠ 0, x} respectively
We know that f (x) is a periodic function

Mathematical analytic function, but not set!
It is known that the domain of F (x) is (x belongs to R and X is not equal to 0) and satisfies 2F (x) + F (one of x) = X
Finding the analytic expression of F (x)
X is case insensitive!

F (x) + 2F (1 / x) = x f (1 / x) + 2F (x) = 1 / X f (x) + 2F (1 / x) = x 2F (1 / x) + 4f (x) = 2 / X - 3f (x) = X-2 / XF (x) = 2 / (3 * x) - X / 3 the equation holds for all real numbers

100 points to ask 2 math senior one function questions to add instructions!
1. Let the even function f (x) defined on [- 2.2] be reduced on the interval [0,2], if
F（1-M）

1 Analysis: according to the even function, and the simple reduction in the interval [0,2], we can know that the monotone increase in [- 2,0], and then discuss according to the different situations of 1-m and m in the two intervals
F (1-m)