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How to solve this limit $\displaystyle\lim\limits_{x \to \infty} \left(-2x - \sqrt{4x^2 +1}\right)$ and when $x\to-\infty$

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closed as off-topic by Goos, T. Bongers, Macavity, vadim123, RecklessReckoner May 25 at 5:10

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1  
What do you think? –  Awesome May 6 at 11:17
    
How to find the limit –  user2685833 May 6 at 11:18
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What have you tried? –  Awesome May 6 at 11:18
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Take the 4x^2 out of the root and observe –  user142634 May 6 at 11:19
    
I have tried, and get 0/0 form –  user2685833 May 6 at 11:21

1 Answer 1

Hint: Amplify by its conjugate, $-2x+\sqrt{4x^2+1}$, and see what you get.

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I get $\frac{1}{-2x+\sqrt{4x^2+1}}$ , and * 1/x and get 0/0 form. –  user2685833 May 6 at 11:54
    
It's not a $\dfrac00$ form, since x tends to MINUS infinity. –  Lucian May 6 at 12:17

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