anonymous
  • anonymous
why doesnt the limit of 2x-12/|x+6| exist as you approach -6
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
because if x=-6 and u input that in the absolute value ur gonna get 0. when u muiltiply the rest by 0 u get 0
anonymous
  • anonymous
i guess i shouldnt have asked it like that because i understand that consept... my prof gave a hint and it says to evaluate the limit from the left and right
anonymous
  • anonymous
Split the absolute value sign into two parts.

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anonymous
  • anonymous
\[ \frac{2x-12}{x+6}\quad \frac{2x-12}{-(x+6)} \]
anonymous
  • anonymous
Suppose \[ \lim \frac{2x-12}{x+6} = L \]Then \[ \lim \frac{2x-12}{-(x+6)} = -L \]
anonymous
  • anonymous
The only way for a limit to exist is if \(L = -L\).
anonymous
  • anonymous
Or, basically it must be the case that \(L=0\).
anonymous
  • anonymous
We can solve the limit using l'Hospital's rule: \[ \lim \frac{2x-12}{x+6} = \lim \frac{(2x-12)'}{(x+6)'}= \lim \frac{2}{1} = 2 \]
anonymous
  • anonymous
Since \(L=2\neq 0\) the limit doesn't exist.

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