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Let $f$ be the real valued function on $[0, \infty)$ defined by

$f(x) = \begin{cases} x^{\frac{2}{3}}\log x& \text {for x > 0} \\ 0& \text{if x=0 } \end{cases}$

Then

1. $f$ is discontinuous at $x = 0$
2. $f$ is continuous on $[0, \infty)$, but not uniformly continuous on $[0, \infty)$
3. $f$ is uniformly continuous on $[0, \infty)$
4. $f$ is not uniformly continuous on $[0, \infty)$, but uniformly continuous on $(0, \infty)$.
asked in Calculus | 44 views