For the scantron-based (*sigh*) final of my high school calculus class, one of the problems was to evaluate(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\lim_{x\to 4^+}\sqrt{4-x}[/tex].

I answered "undefined", reasoning that since [tex]\sqrt{4-x}[/tex] is undefined for all x "to the right of" 4, it could hardly approach any value as x approaches 4 from the right.

More formally, if the limit exists then there is some number L such that for any strictly postive number [tex]\epsilon[/tex], there is a strictly postive number [tex]\delta[/tex] such that

[tex]|\sqrt{4-x}-L|<\epsilon[/tex] whenever [tex]4<x<4+\delta[/tex]. Since x is always greater than 4, [tex]|\sqrt{4-x} - L|[/tex] is undefined (because negative numbers are not in the domain of the square root function) and therefore not less than [tex]\epsilon[/tex]. This leads to a contradiction, therefore there is no limit as x approaches 4 from the right.

My teacher disagreed and said that if the scantron marked me wrong, I must be wrong. She had very little time to listen to me as she had to go eat lunch or something.

Is there anything wrong with my reasoning, or am I right? My final grade in the class could depend on this, so if I'm not mistaken somewhere I plan on confronting my teacher about it after winter break.

Thank you.

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# Undefined limit?

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