Show that the `lim_(xto2) ((sqrt(1-cos{2(x-2)}))/(x-2))` doesnot exist.

Answer

B

Explanation

`underset(xto2)lim((sqrt(1-cos2(x-2)))/(x-2))=underset(xto2)lim(sqrt(2)|sin(x-2)|)/(x-2)`
Now, `underset(xto2^(+))lim(sqrt(2)|sin(x-2)|)/(x-2)=underset(xto2^(+))lim(sqrt(2)sin(x-2))/(x-2)=sqrt(2)`
and `underset(xto2^(-))lim(sqrt(2)|sin(x-2)|)/(x-2)=underset(xto2^(-))lim(-sqrt(2)sin(x-2))/((x-2))=-sqrt(2)`
Hence, limit does not exist.