Statement-1 : `lim_(x to 0) (sqrt(1 - cos 2x))/(x)` at (x = 0). Right and limit `!=` hand limit

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

Evaluate the limits : lim_(x to 0) (sqrt(1+x)-1)/x

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Evaluate the limits lim_(x to 0) (1-cos^2x)/(x sin 2x)

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Evaluate the following limits : Lim_(x to 0) (1-cos 2x)/(x^(2))

Evaluate the following limits : Lim_(x to 0) (sin 2x (1- cos 2x))/(x^(3))

Evaluate the following limit : lim_(x rarr 0) (sqrt(1+x)-1)/(x) .

Solve the limit ; lim_(xto0)((x)/(sqrt(1+x)-sqrt(1-x)))