What's the value of the following limit?
#lim_(x->0)(1 - cos^n(x))/x^2 , n\in N ,n>=1#
1 Answer
Mar 5, 2018
Explanation:
For
# = ((1+cosx)(1-cosx)(1+cosx+cos^2x + * * * +cos^(n-1)x))/((1+cosx)x^2)#
# = ((sin^2x)(1+cosx+cos^2x + * * * +cos^(n-1)x))/(x^2(1+cosx))#
# = (sinx/x)^2(1+cosx+cos^2x + * * * +cos^(n-1)x)/(1+cosx)#
Now evaluate the limit as