Suppose f(x) is defined as shown below. a. Use the continuity checklist to show that f is not continuous at 3. b. Is f continuous from the left or right at 3? c. State the interval(s) of continuity. x2 +2x if x>3 f(x) = . 2x if xs3 a. Why is f not continuous at 3? O A. f(3) is not defined. O B. Although lim f(x) exists, it does not equal f(3). X-3 O C. lim f(x) does not exist. X3 b. Choose the correct answer below. O A. fis continuous from the right at 3. O B. fis continuous from the left at 3, O C. fis not continuous from the left or the right at 3. c. What are the interval(s) of continujty? (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.)

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.