# Math Help - How do you find the limit of this trig. function?

1. ## How do you find the limit of this trig. function?

lim x-->0 [4x+sin(6x)]/[x-tan(5x)]
x is theta

I tried this:
4/1 lim x->0 [x+sin(6x)]/[x-tan 5x]
4/1 lim x->0 [x(1+[sin(6x)/x])/[x-(sin(5x)/cos(5x))]
4/1 lim x->0 [x(1+[sin(6x)/x])/[x(1-[sin(5x)/x]*(1/cos(5x))]
4/1 * 6/5 lim x->0 [1+(sin(6x)/6x)]/[(sin(5x)/5x)*(1/cos(5x))]

I'm not sure if I did the steps right because I cannot seem to get the right answer.

2. Originally Posted by laila
lim x-->0 [4x+sin(6x)]/[x-tan(5x)]
x is theta

I tried this:
4/1 lim x->0 [x+sin(6x)]/[x-tan 5x]
4/1 lim x->0 [x(1+[sin(6x)/x])/[x-(sin(5x)/cos(5x))]
4/1 lim x->0 [x(1+[sin(6x)/x])/[x(1-[sin(5x)/x]*(1/cos(5x))]
4/1 * 6/5 lim x->0 [1+(sin(6x)/6x)]/[(sin(5x)/5x)*(1/cos(5x))]

I'm not sure if I did the steps right because I cannot seem to get the right answer.
Have you been taught l'Hopital's Rule?