Fin # lim_(x rarr 0) ((cotx)(1-cos2x))/x =2 #?
1 Answer
Sep 28, 2017
# lim_(x rarr 0) ((cotx)(1-cos2x))/x =2 #
Explanation:
We seek:
# L = lim_(x rarr 0) ((cotx)(1-cos2x))/x #
# \ \ = lim_(x rarr 0) ((cosx/sinx)(1-(cos^2x-sin^2x)))/x #
# \ \ = lim_(x rarr 0) (cosx/sinx)((1-(1-sin^2x-sin^2x)))/x #
# \ \ = lim_(x rarr 0) (cosx/sinx)((2sin^2x))/x #
# \ \ = lim_(x rarr 0) (cosx) (2sinx)/x #
# \ \ = 2 lim_(x rarr 0) (cosx) ((sinx)/x) #
# \ \ = 2{ lim_(x rarr 0) (cosx)}{ lim_(x rarr 0) ((sinx)/x)} #
# \ \ = 2 * 1 * 1 #
# \ \ = 2 #
