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Which of the following statements is TRUE for the function:

$$g(x)=1+\sqrt[4]{x^4+0.01}$$

I. $\lim \limits_{x \to 0} g(x)=g(0)$II. $g(x)$ has a horizontal tangent at $x=0$III. $g’(0)$ does not exist

I only.

II only.

I and II only.

I and III only.