Statement -1 : `lim_(xrarralpha) sqrt(1-cos 2(x-alpha))/(x-alpha)` does not exist.
Statement-2 : `lim_(xrarr0) (|sin x|)/(x)` does not exist.

Options

A. Statement -1 is true, Statement-2 is true,, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for statement -1.
C. Statement-1 is true, Statement-2 is False.
D. Statement-1 is False, Statement-2 is true.

Answer

A

Explanation

We know that
`lim_(xto0^-)(|sin|)/(x) =lim_(xto0^-)(-sin x) /(x)=-`
and,
`lim_(xto0^-) (|sin|)/(x)=lim_(xto0^-)(sinx)/(x)=1`
`rArr lim_(xto0) (|sin|)/(x) ` does not exist
So, statement-2 is true.
` lim_(xtoalpha) sqrt(1-cos 2(x-alpha))/(x-alpha)=lim_(xtoalpha) (|sin(x-alpha)|)/(x-alpha)`
` lim_(xtoalpha) sqrt(1-cos 2(x-alpha))/(x-alpha)"does not exist".["Using state-2"]`
So, both the statements are true and statement-2 is a correct explanation for statement -1.