Short Answer

State what it means for a function f to be left continuous at a point x = c, in terms of the delta–epsilon definition of limit.

The function f to be left continuous at a point x = c, in terms of the delta–epsilon definition of limit is $\lim_{x \to c} f (x) = L$ for all number $ε > 0,$ there exists some real number $δ > 0$ such that if $x \in (c - δ, c)$ we have $f (x) \in (f (c) - ε, f (c) + ε) .$

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Step 1. Given Information.

The function f is left continuous at a point x=c.

Step 2. Stating.

The function f to be left continuous at a point x = c, in terms of the delta-epsilon definition of limit.

Let f(x) be a function defined on the interval that contains x=c, then the limit $\lim_{x \to c} f (x) = L$ for all number $ε > 0,$ there exists some real number $δ > 0$ such that if $x \in (c - δ, c)$ we have $f (x) \in (f (c) - ε, f (c) + ε) .$

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Calculus

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Short Answer

State what it means for a function f to be left continuous at a point x = c, in terms of the delta–epsilon definition of limit.

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Step 1. Given Information.

Step 2. Stating.

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Calculus

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Short Answer

State what it means for a function f to be left continuous at a point x = c, in terms of the delta–epsilon definition of limit.

Step by Step Solution

Step 1. Given Information.

Step 2. Stating.

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