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by **AdvoTV** on Thu Dec 31, 2009 3:29 am

Hello, I'm having a problem with this limit, and any help you could all provide would be much appreciated.

Prove that if

$\lim_{x\to{c}}f(x)=L$ ,

then

$\lim_{x\to{c}}|f(x)|=|L|$ .

Hint: Use the reverse triangle inequality

$|f(x)|-|L|\leq{|f(x)-L|}$

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by **Martingale** on Tue Jan 05, 2010 3:06 am

AdvoTV wrote:Hello, I'm having a problem with this limit, and any help you could all provide would be much appreciated.

Prove that if

$\lim_{x\to{c}}f(x)=L$ ,

then

$\lim_{x\to{c}}|f(x)|=|L|$ .

Hint: Use the reverse triangle inequality

$|f(x)|-|L|\leq{|f(x)-L|}$

http://en.wikipedia.org/wiki/Triangle_inequality#Reverse_triangle_inequality

$\left||f(x)|-|L|\right|\leq|f(x)-L|$

Use the standard $\epsilon,\delta$ definition of a limit.

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