Find the limit of $x+\sqrt{x^2+3}$ as $x$ approaches $- \infty $

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Step-by-step Solution

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  • Solve using L'Hôpital's rule
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  • Solve using limit properties
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  • Solve the limit using factorization
  • Solve the limit using rationalization
  • Integrate by partial fractions
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Applying rationalisation

$\lim_{x\to{- \infty }}\left(\left(x+\sqrt{x^2+3}\right)\frac{x-\sqrt{x^2+3}}{x-\sqrt{x^2+3}}\right)$

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$\lim_{x\to{- \infty }}\left(\left(x+\sqrt{x^2+3}\right)\frac{x-\sqrt{x^2+3}}{x-\sqrt{x^2+3}}\right)$

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Learn how to solve limits to infinity problems step by step online. Find the limit of x+(x^2+3)^(1/2) as x approaches -infinity. Applying rationalisation. Multiply and simplify the expression within the limit. Cancel like terms x^2 and -x^2. Evaluate the limit \lim_{x\to{- \infty }}\left(\frac{-3}{x-\sqrt{x^2+3}}\right) by replacing all occurrences of x by - \infty .

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Function Plot

Plotting: $x+\sqrt{x^2+3}$

Main Topic: Limits to Infinity

The limit of a function f(x) when x tends to infinity is the value that the function takes as the value of x grows indefinitely.

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