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lim(x rarr 2)(sqrt(1-cos{2(x-2)})/(x-2))...

`lim_(x rarr 2)(sqrt(1-cos{2(x-2)})/(x-2))` =?

Text Solution

Verified by Experts

The correct Answer is:
B
`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.
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