Squeeze theorem: set up inequalities putting the function of interest between two integers.
L'Hopital's rule: when plugging in the number into the limit results in a specified indeterminate form such as 0/0 or infinity/infinity then take the derivative of the numerator and the derivative of the denominator and again plug-in to solve the limit.
The limit of 1-cosx/x as x --> 0 is 1.
The Attempt at a Solution
I used L'Hopital's rule and applied two iterations of get
Plugging in 0 results in
1 / (4+4-0) = 1/8
However, we never learned L'Hopital's rule in class and the only thing we learned was the squeeze theorem. I attempted to use the squeeze theorem (without success):
I'm not sure where to proceed beyond the above step in using the squeeze theorem.
x--> 0 so infinity≤(1-cosx)/x≤infinity
Is the squeeze theorem the correct method to solve this problem? Or am I overlooking some common identity or method other than L'Hopital's rule to solve this problem?