Statement I: `lim_(x->0)x/(sinb^2x)=4` then `b=+-1/2` Statement II: `lim_(x->0) sinx/x=1`

Statement 1: lim_(xto0)[(sinx)/x]=0 Statement 2: lim_(xto0)[(sinx)/x]=1

Statement 1: lim_(xto0)[(sinx)/x]=0 Statement 2: lim_(xto0)[(sinx)/x]=1

Statement - I: if lim_(x to 0)((sinx)/(x)+f(x)) does not exist, then lim_(x to 0)f(x) does not exist. Statement - II: lim_( x to 0)(sinx)/(x)=1

Statement-1 : lim_(x to 0) (1 - cos x)/(x(2^(x) - 1)) = (1)/(2) log_(2) e . Statement : lim_(x to 0) ("sin" x)/(x) = 1 , lim_(x to 0) (a^(x) - 1)/(x) = log a, a gt 0

Statement-1 : lim_(x to 0) (1 - cos x)/(x(2^(x) - 1)) = (1)/(2) log_(2) e . Statement : lim_(x to 0) ("sin" x)/(x) = 1 , lim_(x to 0) (a^(x) - 1)/(x) = log a, a gt 0

lim_(xrarr0) (x^(2)-x)/(sinx)

lim_(xrarr0) (x^(2)-x)/(sinx)

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

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

Let f(x) = {{:((cos x-e^(x^(2)//2))/(x^(3))",",x ne 0),(0",",x = 0):} , then Statement I f(x) is continuous at x = 0. Statement II lim_(x to 0 )(cos x-e^(x^(2)//2))/(x^(3)) = - (1)/(12)