1. The problem asks to find values of $a$ where the function $g$ has different behaviors regarding the limit and value of $g(a)$. We analyze each part based on the graph description. 2. (a) $\lim_{x \to a} g(x)$ does not exist but $g(a)$ is defined. - At $x=2$, there is an open circle at a local maximum (limit value) and a filled circle below it (defined value). This means $g(2)$ is defined but the limit from both sides does not match or is not equal to $g(2)$, so limit does not exist. 3. (b) $\lim_{x \to a} g(x)$ exists but $g(a)$ is not defined. - At $x=4$, the graph shows two open circles connected by a curve with a jump discontinuity. Both one-sided limits exist but differ, so limit does NOT exist. - At $x=6$, there is a filled circle above the curve end and the left-hand limit exists. - Since the limit must exist, the only candidate where limit exists but $g(a)$ is not defined (no filled circle) is none clearly from the description, but typically the limit exists where one-sided limits equal and no point is defined. Given $x=4$ has no filled circle, but limit does NOT exist, so no answer there. - Alternative might be $x=6$ if the limit from the left exists but $g(6)$ is defined (filled circle) so no. So no $a$ matches exactly here unless more info. 4. (c) $\lim_{x \to a^-} g(x)$ and $\lim_{x \to a^+} g(x)$ both exist but $\lim_{x \to a} g(x)$ does not exist. - This occurs at jump discontinuities. - At $x=4$, the two open circles mean left and right limits exist but differ, so limit does not exist. - Smaller value for $a = 4$, larger value for $a$ is not specified for another jump. 5. (d) $\lim_{x \to a^+} g(x) = g(a)$ but $\lim_{x \to a^-} g(x) \neq g(a)$. - At $x=6$, the filled circle is above curve end which means $g(6)$ is defined, left-hand limit exists but not equal to $g(6)$. Final answers: (a) $a = 2$ (b) No value satisfies the condition based on description. (c) $a = 4$ (d) $a = 6$