Monday, 7 October 2013

calculus - How do I find this limit: limxtoinftysqrtx43x21x2




lim



The answer is
\frac{-3}{2}
according to Wolfram alpha.


Answer



I would consider \lim_{x \to \infty} \sqrt{x^4-3x^2-1}-x^2

as \lim_{x \to \infty} \dfrac{\sqrt{x^4-3x^2-1}-x^2}{1}



Then multiply \sqrt{x^4-3x^2-1}+x^2 top and bottom to get rid of the ridiculous looking square root sign on the top. Then bingo!


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