Wie berechnet man das Limit von # tanx / x # als # x-> 0 #?

#lim_(xrarr0) tanx/x = lim_(xrarr0) (sinx/cosx)/x#

# = lim_(xrarr0) sinx/(xcosx)#

# = lim_(xrarr0) (sinx/x*1/cosx)#

# = lim_(xrarr0) (sinx/x) *lim_(xrarr0)(1/cosx)# (provided that both limits exist)

# = (1)(1/1) = 1#