JEE Main 20199 Apr, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002If f(x)=[x]−[x4]f(x) = [x] - \left[ {{x \over 4}} \right]f(x)=[x]−[4x] ,x ∈\in∈ 4 , where [x] denotes the greatest integer function, thenAOption A. Both limx→4−f(x)\mathop {\lim }\limits_{x \to 4 - } f(x)x→4−limf(x) and limx→4+f(x)\mathop {\lim }\limits_{x \to 4 + } f(x)x→4+limf(x) exist but are not equalBOption B. f is continuous at x = 4COption C. limx→4+f(x)\mathop {\lim }\limits_{x \to 4 + } f(x)x→4+limf(x) exists but limx→4−f(x)\mathop {\lim }\limits_{x \to 4 - } f(x)x→4−limf(x) does not existDOption D. limx→4−f(x)\mathop {\lim }\limits_{x \to 4 - } f(x)x→4−limf(x) exists but limx→4+f(x)\mathop {\lim }\limits_{x \to 4 + } f(x)x→4+limf(x) does not existCheckSkip · show solution
