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AP® Calculus AB-BC

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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

A

I only

B

II only

C

I and II only

D

I and III only