Question

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

Answer 1

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