Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

$f$ is a piecewise function defined as $f(x)=x$ if $x\not= 2$, and $f(x)=5$ if $x=2$. What is the limit of $f$ as $x$ approaches $2$? Is the answer $2$ or $5$? I'm guessing the answer is $2$ but am I correct or wrong?

share|improve this question
    
Do you know the $\varepsilon-\delta$ definition of a limit? –  Michael Albanese Jan 22 '13 at 12:01
1  
The point of a limit is that it gives you information about the function near $x=2$, not at $x=2$. –  Michael Albanese Jan 22 '13 at 12:08

1 Answer 1

up vote 3 down vote accepted

Go back to the definition of a limit.

Approach from the left side and the right side.

A limit of a real function is just the value of $f$ as you approach the point of interest. It's not the value of f AT the point of interest. This is true only if f is continuous there.

If you approach from the left, the value of your function approaches $2$. If you approach from the right, the value of your function approaches $2$. You can prove this by using the $\epsilon$ /$\delta$ definition (which will be defined in any calculus/analysis book)

So your answer should be $2$ !

share|improve this answer
    
Thank you! $[][][][][]$ –  Ryan Jan 22 '13 at 12:07

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.