Squeeze theorem If h(x)<= f(x)<= g(x) And lim_(x -> a)h(x)=L And lim_(x -> a)g(x)=L Then lim_(x -> a)f(x)=L -1<= cos ((2)/(x))<= 1 Multiply Throughout by x^(4), To get -x^(4)<= x^(4)cos ((2)/(x))<= x^(4) Since, lim_(x -> 0)-x^(4)=0 And, lim_(x -> 0)x^(4)=0 By Squeeze Theorem, We have lim_(x -> 0)x^(4)cos ((2)/(x))=0 Result: lim_(x -> 0)x^(4)cos ((2)/(x))=0