Limit of sin x/x as x Tends to Zero
Limit of sin x/x as x Tends to Zero
Express as tanx≥x≥sinx. Divide by sinx and take reciprocals to get . Since , by the squeeze theorem, =1.
ΔOPM>sector(OPQ)>ΔOPQ
1
2
1
2
1
2
1
2
cosx≤≤1
sinx
x
cos0=1
lim
x0
sinx
x
This is the only limit needed to get the derivatives of all the trigonometric functions and their inverses.