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Use the definition of continuity and the properties of limits to show that the function

f(x) = x2 + 5(x - 2)7 is continuous at x = 3.

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Answer:

Applied the definition and the limit.

They had the same result, so the function is continuous.

Explanation:

At function f(x) is continuous at x = a if:


\lim_(x \to a) f(x) = f(a)

In this question:


f(x) = x^(2) + 5(x-2)^(7)

At x = 3.


\lim_(x \to 3) x^(2) + 5(x-2)^(7) = 3^(2) + 5(3-2)^(7) = 14


f(3) = 3^(2) + 5(3-2)^(7) = 14

Since
\lim_(x \to 3) f(x) = f(3), f(x) is continuous at x = 3.

User Adam Milligan
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