2 Use the definition of continuity to show f (x) = is x+3 continuous at x=1. Whenever you find a limit, use Limit Laws only and justify each step by stating the appropriate Limit Law used.

Q: If a function f has no limit as x approaches c, then we say that lim f(x)

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Q: Assume the given function in each part is continuous everywhere. Determine what graphical feature is…

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Q: -12 |–10 -8 -6 F4 4 10 12 2, 2.

A: The given graph of the function f(x) is

Q: Vx + 4 – 2 Use a table of values to estimate the value of the limit of lim f(x) f(x) ERSIT 2.

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Q: Explain, using limit definition, why f′(x) = 0 for any constant function f(x) = c.

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Q: Identify a use of the lower and upper limits.

A: The lower and upper limits of the data set will not be plotted in the box plot.

Q: Let f(x) = 2x2 +1. Evaluate f(4 + h) - f(4) lim h-0 h

A: Given, The function f(x)=2x2+1.

Q: The L'Hospital's rule can be applied to find the limit of a function as long as you can express it…

A: L'Hospital's rule states that, the limit of the ratio of two functions is equal to the limit of the…

Q: Find the value k that makes the function continuous. kx f (x) = x > 9 - -7x – 7, x < 9

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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.