Find the limit.
lim sin(6x) / x + tan(9x)
x→0
When theta is very small then sin(theta) → theta, and tan(theta)→theta
So sin(6x)/x + tan(9x) → 6x/x + 9x = 6 + 0 = 6 as x tends to zero
I think this also might be
lim sin(6x) / [ x + tan(9x) ]
Using L'Hopital's Rule we have
lim 6cos(6x) /[ 1 + 9sec^2(9x) ] = 6(1) / [ 1 + 9 ] = 6 /10 = 3 / 5
