Evaluate the limit #lim_(x rarr pi) sin^2 (4x) / tan^2 (4x) #?
1 Answer
Sep 15, 2017
# lim_(x rarr pi) sin^2 (4x) / tan^2 (4x) = 1#
Explanation:
We seek:
# L= lim_(x rarr pi) sin^2 (4x) / tan^2 (4x) #
# \ \ = lim_(x rarr pi) sin^2 (4x) / (sin^2(4x)/cos^2 (4x) )#
# \ \ = lim_(x rarr pi) sin^2 (4x) (cos^2(4x)/sin^2 (4x) )#
# \ \ = lim_(x rarr pi) cos^2(4x)#
# \ \ = cos^2(4pi)#
# \ \ = 1#
