極限の一覧
lim x → 0 sin  x x = 1 {\displaystyle \lim _{x\to 0}{\frac {\sin x}{x}}=1}
lim x → a sin  x = sin  a {\displaystyle \lim _{x\to a}\sin x=\sin a}
lim x → a cos  x = cos  a {\displaystyle \lim _{x\to a}\cos x=\cos a}
lim x → n ± 0 tan  ( π x + π 2 ) = ∓ ∞ for any integer n {\displaystyle \lim _{x\to n\pm 0}\tan \left(\pi x+{\frac {\pi }{2}}\right)=\mp \infty \qquad {\mbox{ for any integer }}n}