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Numerade Educator

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Problem 46 Medium Difficulty

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. If l'Hospital's Rule doesn't apply, explain why.

$ \displaystyle \lim_{x\to -\infty} x\ln \left( 1 - \frac{1}{x} \right) $

Answer

$-1$

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Video Transcript

So this problem we're gonna be using luke tells role in order to determine the limit of the function. So uh here are function is X times the natural log of one minus, so X times natural log of one minus one over X. Mhm. So this can be rewritten um as this right here divided by one over X. And the reason we do this is so that way we can substitute T to equal one over X. That way as x goes to infinity, t goes to zero. So now when we evaluate this we get 0/0. That's the indeterminant form, but we can take the derivative of it and that will end up giving us one down here. Uh This will give us a negative 1/1 -1 key. That's an ultimately going to be negative 1/1 0. That'll be negative one as our final answer.