Difficult# Functions with an Interesting Point at $x = 0$

APCALC-YEZN9S

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