Let `f(x) = cos(x cos(1/x))` Statement-1 : `f(x)` is discontinuous at `x = 0`. Statement-2: `Lim-(x->0) f(x)` does not exist.

Show that the function f(x) = x cos (1//x), x ne 0 f(0) = 1 is discontinuous at x = 0.

Statement - 1: The function f(x) = {x}, where {.} denotes the fractional part function is discontinuous a x = 1 Statement -2: lim_(x->1^+) f(x)!= lim_(x->1^+) f(x)

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)

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)

Statement I f(x) = sin x + [x] is discontinuous at x = 0. Statement II If g(x) is continuous and f(x) is discontinuous, then g(x) + f(x) will necessarily be discontinuous at x = a.

Statement I f(x) = sin x + [x] is discontinuous at x = 0. Statement II If g(x) is continuous and f(x) is discontinuous, then g(x) + f(x) will necessarily be discontinuous at x = a.

Statement I f(x) = sin x + [x] is discontinuous at x = 0. Statement II If g(x) is continuous and f(x) is discontinuous, then g(x) + f(x) will necessarily be discontinuous at x = a.

Let f(x)=\ {x+5,\ if\ x >0 and x-4,\ if\ x 0)\ f(x) does not exist.

Let f(x)={(1-cos x)/(x^(2)), when x!=01,quad when x=0. Show that f(x) is discontinuous at x=0 .