find the limit

Ltx-0sin2x/3x

Hi!
 
lim x → 0 (sin 2x/sin 3x)

 
Thus, the value of the expression lim x → 0 (sin 2x/sin 3x) is 2/3.
Cheers!

  • 1

Ltx-0 sin2x/3x

multiply and divide by 2

Ltx-0 2/3 sin2x/2x

= 2/3 ans.

  • 2

lim x->0  (sin 2x) / 3x = lim x->0 (2/3 * sin2x) / (2/3*3x)

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

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