Exercise · ZW-CONTINUOUS-FUNCTION-011 · ★☆☆ Basic
For \(f(x)=2x-5\) at \(c=3\) and \(\varepsilon=0.4\), what is the largest \(\delta\) that works?
Choose one option.
Show answer
- B. \(\delta=0.2\)
Explanation
Since \(|f(x)-f(3)|=2|x-3|\), we need \(2\delta\le0.4\), that is \(\delta=0.2\). Using \(0.4\) ignores the factor \(2\).
Review the concept: Continuous function
A function \(f\) is continuous at \(a\) if \(f(a)\) is defined, its limit as \(x\) tends to \(a\) exists and equals \(f(a)\).
\[\lim_{x\to a}f(x)=f(a)\]
More practice problems: continuous function
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- ZW-CONTINUOUS-FUNCTION-006 Which value of k makes f(x)=(x^2-9)/(x-3) continuous at x = 3 when x≠3 and f(3)=k?
- ZW-CONTINUOUS-FUNCTION-007 Which value of k makes continuous at x = 1 the function defined by f(x)=x+k if x<1 and f(x)=2x^2 if…
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