Suppose f(x) is defined as shown below. a. Use the continuity checklist to show that f is not continuous at 2. b. Is f continuous from the left or right at 2? c. State the interval(s) of continuity. $\begin{aligned} f(x) = \begin{cases} x^2+3x & \text{if } x>2\\ 4x & \text{if } x \le 2 \end{cases} \end{aligned}$ a. Why is f not continuous at 2? A. $\lim_{x \to 2} f(x)$ does not exist. B. f(2) is not defined. C. Although $\lim_{x \to 2} f(x)$ exists, it does not equal f(2). b. Choose the correct answer below. A. f is continuous from the right at 2. B. f is not continuous from the left or the right at 2. C. f is continuous from the left at 2. c. What are the interval(s) of continuity? (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed)
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2) The limit of f(x) as x approaches 2 exists. 3) The limit of f(x) as x approaches 2 is equal to f(2). Show more…
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