It is proved that the function f (x) = 1 / X is unbounded at (0,1)

It is proved that the function f (x) = 1 / X is unbounded at (0,1)

Proof to the contrary. Suppose bounded, | f (x) | 1
Then t = 1 / (2m),
0

Which of the following functions are periodic? For periodic function, point out its period
（1）y=cos(x-2);
（2）y=cos4s;
（3）y=1+sin（3.1415926…… x);
（4）y=xcosx;
(5) Y = sin ^ 2x (this "2" is in the position of "^")

(1) Is a periodic function, t = 2 π / 1 = 2 π
(2) Is a periodic function, t = 2 π / 4 = π / 2
(3) Is a periodic function, t = 2 π / π = 2
(4) It's not a periodic function
(5) Is a periodic function, y = Sin & # 178; X = (1-cos2x) / 2, t = 2 π / 2 = π

Finding the minimum positive period of the function y = cos3x + sin3x / cos3x-sin3x

y=cos3x+sin3x\cos3x-sin3x
=(1+tan3x)/(1-tan3x)
=-(1-tan3x-2)/(1-tan3x)
=-1+2/(1-tan3x)
3T=∏/2,
T=∏/6
Minimum positive period Π / 6