Use the definition of continuity and the properties of limits to show that the function is continuous on the given interval. f(x) = x + Vx- 9, [9, 0) For a ? v 9, we have lim f(x) - lim (x + Vx - 9) = lim x + lim x→ヨ = lim x + lim - lim 9 x-a x-a + = Therefore, fis continuous at x = a for every a in (9, co). Also, lim f(x) = = f(9), so fis continuous from the right at 9. Thus, f is continuous on [9, co). x-9*

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A: Topic -Limit and continuity

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Q: Prove that a function f is continuous at a limit point p iff the limit as x goes to p is f(p).

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A: [i]

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.