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Published byよしじろう いまいだ Modified over 5 years ago
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A function f is continuous at the point x = a if the following are true:
f(a) a
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Example Continuous everywhere except at
At which value(s) of x is the given function discontinuous? Continuous everywhere Continuous everywhere except at
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F is continuous everywhere else h is continuous everywhere else
and and Thus F is not cont. at Thus h is not cont. at x=1. F is continuous everywhere else h is continuous everywhere else
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Continuous Functions If f and g are continuous at x = a, then
A polynomial function y = P(x) is continuous at every point x. A rational function is continuous at every point x in its domain.
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Overview of Problems 1 2 3 4 5
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Continuity Problem 1 Solution
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Continuity Problem 2 Solution
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Continuity Problem 3 Solution
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Continuity Problem 4 Answer Removable Not removable
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Continuity Problem 5 Solution
By the intermediate Value Theorem, a continuous function takes any value between any two of its values. I.e. it suffices to show that the function f changes its sign infinitely often.
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