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Flashcards: Define Continuity at a Point and Over An Interval

Which of the following is the correct definition of continuity?

A function f(x) is continuous at x = a if $lim_{x\rightarrow \infty} f(x) = f(a)$

A function f(x) is continuous at x = a if $lim_{x\rightarrow 0} f(x) = f(a)$

A function f(x) is continuous at x = a if $lim_{x\rightarrow a} f(x) = f(a)$

A function f(x) is continuous at x = a if $lim_{a\rightarrow x} f(x) = f(a)$

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Flashcards: Define Continuity at a Point and Over An Interval

Which of the following is the correct definition of continuity?

Your answer:

A function f(x) is continuous at x = a if $lim_{x\rightarrow \infty} f(x) = f(a)$

Your answer:

A function f(x) is continuous at x = a if $lim_{x\rightarrow 0} f(x) = f(a)$

Your answer:

A function f(x) is continuous at x = a if $lim_{a\rightarrow x} f(x) = f(a)$

Correct answer:

A function f(x) is continuous at x = a if $lim_{x\rightarrow a} f(x) = f(a)$

Explanation:

A function is a continuous function on an interval if it is continuous at each and every point on that interval. You are able to check and see if a function is continuous at certain points using the definition of continuity:

A function f(x) is continuous at x = a if $lim_{x\rightarrow a} f(x) = f(a)$

This definition assumes that both $lim_{x\rightarrow a}$ and f(a) exist. If either of these do not exist or the if $lim_{x\rightarrow a} f(x) \neq f(a)$ , then the function f(x) is not continuous at point and the function is not a continuous function on any interval containing .

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Flashcards: Define Continuity at a Point and Over An Interval

Flashcards: Define Continuity at a Point and Over An Interval

Flashcards: Define Continuity at a Point and Over An Interval

Flashcards: Define Continuity at a Point and Over An Interval

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Flashcards: Define Continuity at a Point and Over An Interval

Flashcards: Define Continuity at a Point and Over An Interval

Flashcards: Define Continuity at a Point and Over An Interval

Flashcards: Define Continuity at a Point and Over An Interval

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