How do you prove that the limit #x^2 cos(1/x) = 0# as x approaches 0 using the formal definition of a limit?
1 Answer
Sep 30, 2016
Please see below.
Explanation:
Given
Now, if
then
# = x^2 abs( cos(1/x))#
# <= x^2 (1)#
# < (sqrt epsilon)^2 = epsilon# .
That is: if
So, by definition of limit,