Find the limit?
#lim_(nrarr oo)x_n#
where
#x_n=root(3)((n^2)-(n^3))+n#
where
2 Answers
Explanation:
Assuming the limit as
now calling
Please see below.
Explanation:
Use
# = (n^2-n^3+n^3)/ ((root(3)(n^2-n^3))^2 - nroot(3)(n^2-n^3)+n^2)#
# = n^2/ (n^2(root(3)(1/n-1))^2 - n^2root(3)(1/n-1)+n^2)#
# = 1/ ((root(3)(1/n-1))^2 - root(3)(1/n-1)+1)#
So,
# = 1/ ((root(3)(0-1))^2 - root(3)(0-1)+1)#
# = 1/ ((-1)^2 - (-1)+1)#
# = 1/3#