1 Answers

Best Answer

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