Also known as the Squeeze Theorem
and/or the Pinch Theorem
If f(x) <= g(x) <= h(x) on a function approaching x, and the limit as x approaches c of f(x) and h(x) both equal L, then the limit as x approaches c of g(x)=L.
limit as x->0 of sin(1/x)
Given:-1 is less than or equal to x sin(1/x) is less than or equal to 1
Apply the limit to f(x)and you get an undefined value.
Multiply the left and right values by any coefficient in the sandwiched function(in this case x). Apply the limit to the values on the left and right sides of the sandwiched value. The result will be your solution.
limit as x->0 of -x = 0
limit as x->0 of x = 0
Your solution is 0