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Limits Continuity and Differentiability question

2019 · 9 Apr · Shift 2 · Q37

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JEE Main
Mathematics
Limits Continuity and Differentiability
2019 · 9 Apr · Shift 2 · Q37

Limits Continuity and Differentiability question

2019 · 9 Apr · Shift 2 · Q37

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

If

f(x) = [x] - \left[ {{x \over 4}} \right]

,x

\in

4 , where [x] denotes the greatest integer function, then

A
Both $\mathop {\lim }\limits_{x \to 4 - } f(x)$ and $\mathop {\lim }\limits_{x \to 4 + } f(x)$ exist but are not equal
B
f is continuous at x = 4
C
$\mathop {\lim }\limits_{x \to 4 + } f(x)$ exists but $\mathop {\lim }\limits_{x \to 4 - } f(x)$ does not exist
D
$\mathop {\lim }\limits_{x \to 4 - } f(x)$ exists but $\mathop {\lim }\limits_{x \to 4 + } f(x)$ does not exist

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