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Q. 14

Expert-verified
Found in: Page 119

### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

# 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 $\underset{x\to c}{\mathrm{lim}}f\left(x\right)=L$ for all number $\epsilon >0,$ there exists some real number $\delta >0$ such that if $x\in \left(c-\delta ,c\right)$ we have $f\left(x\right)\in \left(f\left(c\right)-\epsilon ,f\left(c\right)+\epsilon \right).$

See the step by step solution

## 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 $\underset{x\to c}{\mathrm{lim}}f\left(x\right)=L$ for all number $\epsilon >0,$ there exists some real number $\delta >0$ such that if $x\in \left(c-\delta ,c\right)$ we have $f\left(x\right)\in \left(f\left(c\right)-\epsilon ,f\left(c\right)+\epsilon \right).$