lims
$ \lim\limits_{x -> 0} \frac{sinx} {x} = $
$ \lim\limits_{x -> \infty} (1 + \frac{1} {x})^x = $
Derivative
$ (x^\alpha)^{(n)} = $
$ (x^n)^{(n)} = $
$ (\frac{1}{x})^{(n)} = $
$ (sinx)^{(n)} $
$ (cosx)^{(n)} $
$ (\frac{1}{x + a})^{(n)} = $
$ (a^x)^{(n)} = $
series
Fourier
$ a_n = $
$ b_n = $
$ f(x) ~ $
Dirichlet
$ S(x) = $ans
lims
1
e
Derivative
$ \alpha(\alpha - 1)(\alpha - 2) … (\alpha - n + 1)x^{\alpha - n} $
n!
$\frac{(-1)^n n!}{x^{n+1}} $
$ sin(x + \frac{n}{2} \pi) $
$ cos(x + \frac{n}{2} \pi) $
$ \frac{(-1)^n n!}{(x + a)^{n+1}} $
$ a^x ln^n a ,(a > 0)$
series
Fourier
$ \frac{1}{l} \int^l_{-l} f(x) cos \frac{n \pi x}{l} dx , n = 0,1,2,3…$
$ \frac{1}{l} \int^l_{-l} f(x) sin \frac{n \pi x}{l} dx, n = 1,2,3…$
$ \frac{a0}{2} + \sum\limits{n = 1}^{\infty}(a_n cos\frac{n \pi x }{l} + b_n sin\frac{n \pi x}{l}) $
当x是f(x)的连续点时，f(x)
当x是f(x)的第一类间断点时, $ \frac{f(x-0) + f(x + 0)}{2} $
English
what if 如果。。。将会。。。有没有这样一种可能……
how 如何，多么
2023_Eng_301(Powered By LQR)
Here is a thrilling scene, featuring two teams racing on dragon boats with crowds of people cheering on the bridge. At the corner of the picture, an old woman is holding her husband’s hand, smiling with satisfaction, expressing her happiness seeing the dragon boat race of their village is getting more and more popular.
The idea of the artist lurking behind the caricature can be perceived as an appreciation of the boosting tourism based on traditional Chinese festival in villages. A majority of relevant departments tend to develop blinking forms of activities while overlooking the very essence of them, leading to the result that commercial interest is overstated and the beauty of conventions are forgotten. This tendency may seem innocuous in the short term, risks erasing the sense of belonging in dwellers’ hearts and jeopardizing the real interactions between people and the past in a larger sense. To address the obstacles met in advancing a county requires a shift in mindset-focusing on the daily lives of the public and the thriving of cultural activities. The responsibility urges city authorities to fulfill their role through leading the trend, establishing proper environment for citizens to enjoy such festivals.
With collective commitment in promoting traditional affairs, we can aspire to see more villages or cities to have significant changes and win both ecologically and admirably.