Calculate # lim_(x rarr 0)x/(sin3x) =1/3 #?
1 Answer
# lim_(x rarr 0)x/(sin3x) =1/3 #
Explanation:
We seek:
# L = lim_(x rarr 0)x/(sin3x) #
# \ \ = 1/3 \ lim_(x rarr 0)(3x)/(sin3x) #
If we put
# L = 1/3 \ lim_(theta rarr 0)(theta)/(sin theta) #
And we know that a standard calculus limit is:
# lim_(theta rarr 0)(sin theta)/(theta) = 1 #
And so
# L = 1/3 \ 1/ (lim_(theta rarr 0)(sin theta)/(theta)) #
# \ \ = 1/3 #