Find the limit of sin (ax) / tan (bx) as x approaches 0.

Lim sin (ax) / tan (bx) = [lim ax. sin (ax) / ax] [bx tan (bx) / bx ]

x approaches 0 x approaches 0

we know that lim sin (ax) / ax = 1, for all value of a, and lim tan (bx) / bx = 1 for all value of b,

so lim sin (ax) / tan (bx) = lim 1 * 1 * ax * bx = lim ab x^2 = ab*0 = 0,

x approaches 0 x approaches 0 x approaches 0