6x + 5x if x <5 Let g(x) = a if x = 5 · Зх + 1 if x> 5 a. Determine the value of a for which g is continuous from the left at 5. b. Determine the value of a for which g is continuous from the right at 5. c. Is there a value of a for which g is continuous at 5? a. The value of a for which g is continuous from the left at 5 is 175. (Simplify your answer.) b. The value of a for which g is continuous from the right at 5 is 16 . (Simplify your answer.) c. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. There is no value of a for which g is continuous at 5 because lim g(x) = and lim g(x) =| %3D X5- X→5+ B. When a= g is continuous at 5 because lim g(x) = and lim g(x) = X→5- x→5+

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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.