If $f(x) = [x] - [\frac{x}{4}]$,$x \in R$,where $[x]$ denotes the greatest integer function,then
- ABoth $\lim_{x \to 4^-} f(x)$ and $\lim_{x \to 4^+} f(x)$ exist but are not equal
- B$\lim_{x \to 4^-} f(x)$ exists but $\lim_{x \to 4^+} f(x)$ does not exist
- C$\lim_{x \to 4^+} f(x)$ exists but $\lim_{x \to 4^-} f(x)$ does not exist
- D$f$ is continuous at $x = 4$
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Let $a, b \in R, (a \ne 0)$. If the function $f$ defined as
$f(x) = \begin{cases} \frac{2x^2}{a}, & 0 \le x < 1 \\ a, & 1 \le x < \sqrt{2} \\ \frac{2b^2 - 4b}{x^3}, & \sqrt{2} \le x < \infty \end{cases}$
is continuous in the interval $[0, \infty)$,then an ordered pair $(a, b)$ is
$f(x) = \begin{cases} \frac{2x^2}{a}, & 0 \le x < 1 \\ a, & 1 \le x < \sqrt{2} \\ \frac{2b^2 - 4b}{x^3}, & \sqrt{2} \le x < \infty \end{cases}$
is continuous in the interval $[0, \infty)$,then an ordered pair $(a, b)$ is
DifficultJEE MAIN 2016
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