What is `lim_(xto0) (2(1-cosx))/(x^(2)` equal to?

Options

A. 0
B. `1//2`
C. `1//4`
D. 1

Answer

D

Explanation

`underset(xto0)lim(2(1-cosx))/(x^(2))=underset(xto0)lim(2.2sin^(2)""(x)/2)/x^(2)`
`=4underset(xto0)lim(sin""(x)/(2))/((x)/(2)xx2).underset(xto0)lim(sin""(x)/(2))/((x)/(2)xx2)`
`=underset(xto0)lim(sin""(x)/(2))/((x)/(2)).underset(xto0)lim(sin""(x)/(2))/((x)/(2))=1xx1=1`