Question

How do you use the Squeeze Theorem to find `limsin(1/x)` as x approaches zero?

Answer 1

The limit `lim_(x->0)sin(1/x)` does not exist. You can proove this taking two sequences such as `a_n=1/(2pin)` and `b_n=1/((2n+1)*pi)` and replacing into the value of x.Hence

`sin(1/(1/((2pin))))=sin(2*pi*n)=1 or -1`.Hence the values of the limits both sequences are different such limit does not exist