A function f: R --> R is said to be continuous at c in R if for all epsilon > 0 there exists a delta > 0 so that |f(c) - f(x)| < epsilon whenever |c - x| < delta. Negate this statement, i.e., state what it means that f is not continuous at c.

Q: f is continuous iff f-1(E) is closed

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A: Function limit and continuity

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A: Given that If f(g(x)) is continuous at 0, then g(x) is continuous at 0

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Q: If f is continuous on [-1, 1] and f(x)dx = 0, then there exists some ce [-1,1] for which f(c) = 0.

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A: As image of a connected set is connected in of every continuous function.

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Q: If n is a positive even integer and f(x) = Vx, then f is continuous everywhere. True False

A: Given that n is a positive integer and f(x)=(x)^1/n.

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A: Hi, you can find the answer in the handwritten form.  Given f(a)=-2  f(b)= 2

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Q: For every continuous function f(x) defined on symmetric interval [a,b]. If f(x) is an even function…

A: Here, the given function f(x) is even. So, f(-x)=f(x)

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A: Let ε &gt; 0 such that g(c) − ε &gt; 0 (for instance one can take ε = g(c)/2).

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Q: Consider the cases: (1) x = -4 (2) x = –2 (3) x = 0 (4) x = 2 (5) x = 4 Part (a) For each case,…

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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.