Question

Find the limit

Answer 1

Welcome to Openstudy!

Answer 2

\[\lim_{x \rightarrow 0}\frac{ \sin 5x }{ \sin 7x }\]

Answer 3

No Problem :P

Answer 4

Youre forced to use identities here it looks like. Youll have to break down the sin5x and sin7x using sum of sines formulas and eventually double angle formulas it looks like.

Answer 5

may i suggest another approach
we know that lim of sin(ax)/ax as x->0 equals 1.

so:

sin(5x)/sin(7x) = (5x)(7x)sin(5x)/[(5x)(7x)sin(7x)] = (5/7)*(7x)sin(5x)/[(5x)sin(7x)] now taking the limit according to the known limit that equals 1 = 5/7