13 Sep '08 18:182 edits

hello,

here is the question

Find the Limit of sin2x/sin3x as x approaches 0

i have it started:

start by breaking it up

sin2x*( 1/sin3x)

(3x/2x)*(sin2x)*(1/sin3x)*(2/3)

(2/3)*(sin2x/2x)*(3x/sin3x)

(2/3)*(1)*(3x/sin3x)

in the next step, am I allowed to assume that the limit of (3x/sin3x) is the recipricol of the limit of (sin3x/3x) = 1/1=1, or am i missing another manipulation?

here is the question

Find the Limit of sin2x/sin3x as x approaches 0

i have it started:

start by breaking it up

sin2x*( 1/sin3x)

(3x/2x)*(sin2x)*(1/sin3x)*(2/3)

(2/3)*(sin2x/2x)*(3x/sin3x)

(2/3)*(1)*(3x/sin3x)

in the next step, am I allowed to assume that the limit of (3x/sin3x) is the recipricol of the limit of (sin3x/3x) = 1/1=1, or am i missing another manipulation?