Expert: Paul Klarreich - 2/7/2010

Question
lim theta->0 (sin(theta))/(sin2(theta))

which led me to get:
sin 0/ sin 2*0 = sin 0/sin0 = 1?

Answer
Questioner: ekta
Country: United States
Category: Calculus
Private: No
Subject: calculus -12th grade
Question: lim theta->0 (sin(theta))/(sin2(theta))

which led me to get:
sin 0/ sin 2*0 = sin 0/sin0 = 1
.....................................

Which is wrong, as you already found out.

You must match this result:
      sin t
lim  --------- = 1
t->0     t

and MATCH IT PERFECTLY.  

Try this:

      sin t
lim  --------- =
t->0   sin 2t


      sin t    2t
lim  -------- ------ =
t->0    2t    sin 2t

         sin t          2t
1/2 lim  -------- lim  ------ =
  t->0     t     t->0 sin 2t

                    2t
1/2 (  one  ) lim  ------ =
             t->0 sin 2t

                    y
1/2 (  one  ) lim  ------ =  (where  y = 2t)
             y->0 sin y


                  
1/2 (  one  ) (    one ) =  1/2