Question

Can some one please explain this problem to me?

Find lim x->0 (sin5x/sin7x)

Answer 1

recall that
lim sinØ/Ø = 1 , as Ø----> 0

so we want to make our expression "look like that"

suppose we multiply sin 5x/sin 7x by (7x/5x)*(5x/7x)

so we get
limit [ (sin 5x/(5x) / sin 7x/(7x) ]*(5x)/(7x)
as x---> 0
of course as x---> 0 , so does 5x as well as 7x

= 1/1 * 5/7
= 5/7

you can test this with your calculator,
set it to radians, (the above is true in radians, NOT in degrees)
let x = something like .000001 and evaluate
sin 5x/sin 7x
you will get .714285714
and 5/7 = .714285714 , how about that!