Určení periody funkce
Urči periodu zadané funkce:
\( \large i\left( x\right) = \cos {\Large \frac{2x}{2 \pi+2}\large } \)
\( \frac{2x}{2 \pi\ +\ 2}\ +\ 2k \pi = \frac{2(x\ +\ kp )}{2 \pi\ +\ 1} \)
\( \frac{2x}{2 \pi\ +\ 2}\ +\ 2k \pi = \frac{2x}{2 \pi\ +\ 1}\ +\ \frac{2kp}{2 \pi\ +\ 2} \)
\( 2k \pi = \frac{2kp}{2\pi\ +\ 1} \)
\( 2k \pi(2 \pi\ +\ 1) = 2kp \)
\( p = 2 \pi(\pi) \)
\( \frac{2x}{2 \pi\ +\ 2}\ +\ 2k \pi = \frac{2(x\ +\ kp )}{2 \pi\ +\ 2} \)
\( \frac{2x}{2 \pi\ +\ 2}\ +\ 2k \pi = \frac{2x}{2 \pi\ +\ 2}\ +\ \frac{2kp}{2 \pi\ +\ 2} \)
\( 2k \pi = \frac{2kp}{2\pi\ +\ 2} \)
\( 2k \pi(2 \pi\ +\ 2) = 2kp \)
\( p = 2 \pi(\pi\ +\ 1) \)
\( \frac{2x}{2 \pi\ +\ 2}\ +\ 2k \pi = \frac{2(x\ +\ kp )}{3 \pi\ +\ 2} \)
\( \frac{2x}{2 \pi\ +\ 2}\ +\ 2k \pi = \frac{2x}{3 \pi\ +\ 2}\ +\ \frac{2kp}{2 \pi\ +\ 2} \)
\( 2k \pi = \frac{2kp}{3\pi\ +\ 2} \)
\( 2k \pi(3 \pi\ +\ 2) = 2kp \)
\( p = 3 \pi(\pi\ +\ 1) \)
\( \frac{2x}{2 \pi\ +\ 2}\ +\ 2k \pi = \frac{2(x\ +\ kp )}{2 \pi\ +\ 3} \)
\( \frac{2x}{2 \pi\ +\ 2}\ +\ 2k \pi = \frac{2x}{2 \pi\ +\ 3}\ +\ \frac{2kp}{2 \pi\ +\ 2} \)
\( 2k \pi = \frac{2kp}{2\pi\ +\ 3} \)
\( 2k \pi(2 \pi\ +\ 3) = 2kp \)
\( p = 2 \pi(\pi\ +\ 2) \)