Statement 1: `lim x ->0 ((sqrt(1-cos2x)) logcosx)/x^2` does not exist. Statement 2: `|sinx| = { sinx, 0

Statement-1 : lim_(x to 0) (sqrt(1 - cos 2x))/(x) at (x = 0) does not exist. Statement -2 :Right hand limit != Left hand limit i) Statement - 1 is True, Statement-2 is True, Statement-2 is a correct explanation for statement-1 ii)Statement-1 is True, Statement-2 is True, Statement-2 is Not a correct explanation for statement-1 iii)Statement-1 is True, Statement-2 is False iv)Statement -1 is False, Statement-2 is True

Statement 1:lim_(x rarr0)(sqrt(1-cos2x))/(x) does not existe.Statement 2:f(x)=(sqrt(1-cos2x))/(x) is not defined at x=0

Statement-I underset(x to 0)(Lt)(sqrt((1 -cos 2x)/(2)))/(x) does not exist . Statement-II : f(x) = |x| is continuous on R Which of the above statement is correct

Prove that , underset(x rarr 0)lim (sqrt(1-cos x))/(x) does not exist.

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.

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.

Statement 1: (lim)_(x->0)[x]((e^(1//x)-1)/(e^(1//x)+1)) (where [.] represents greatest integer function) does not exist. Statement 2: (lim)_(x->0)((e^(1//x)-1)/(e^(1//x)+1)) does not exist. Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true; Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true

Statement 1: If lim_(xto0){f(x)+(sinx)/x} does not exist then lim_(xto0)f(x) does not exist. Statement 2: lim_(xto0)((e^(1//x)-1)/(e^(1//x)+1)) does not exist.

Statement 1: If lim_(xto0){f(x)+(sinx)/x} does not exist then lim_(xto0)f(x) does not exist. Statement 2: lim_(xto0)((e^(1//x)-1)/(e^(1//x)+1)) does not exist.

Statement -1 : lim_( x to 0) (sin x)/x exists ,. Statement -2 : |x| is differentiable at x=0 Statement -3 : If lim_(x to 0) (tan kx)/(sin 5x) = 3 , then k = 15