1. **Problem Statement:** Determine from the graph: (a) all values $x=a$ where $\lim_{x \to a} f(x)$ exists but $f$ is not continuous at $x=a$. (b) all values $x=a$ where $f$ is continuous at $x=a$ but not differentiable at $x=a$. 2. **Recall definitions:** - A function $f$ is continuous at $x=a$ if $\lim_{x \to a} f(x) = f(a)$. - If the limit exists but $f(a)$ is not equal to the limit, $f$ is not continuous at $a$. - A function is not differentiable at $a$ if it has a sharp corner or cusp at $a$, even if continuous. 3. **Analyze the graph:** - At $x=1$, the graph shows a jump or mismatch between the limit and function value, so limit exists but not continuous. - At $x=2$, the graph is continuous but has a sharp corner, so continuous but not differentiable. 4. **Conclusion:** - (a) $a=1$ where limit exists but $f$ is not continuous. - (b) $a=2$ where $f$ is continuous but not differentiable. 5. **Answer choice:** This matches option A. Final answer: **A. (a) a = 1 (b) a = 2**