I have a question

Question

how do you find the limit at x approaches 0 of (sin(4x)/sin(7x) without using lhospital rule

Answer 1

Lim_{x->0}( (sin(4x)/sin(7x) )= Lim_{x->0} [(4x*sin(4x)/4x)]/[1/7x*7x/sin(7x)]=

 

Now 

 

Lim_{x->0}(sin(4x)/4x)=1, 

 

Lim_{x->0}(7x/sin(7x)=1,

 

 

So you have the answer 4/7

 

If not clear, let me know.