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Problem 30 Easy Difficulty

Find the limit or show that it does not exist.

$ \displaystyle \lim_{x \to \infty} \sqrt{x^2 + 1} $

Answer

$\infty$

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Video Transcript

To find the limit of the square it of expert plus one. As X approaches infinity, we first factor out the variable with the highest exponent. And so in here we have limit as X approaches infinity of the square it of x squared times one plus one over x squared. And then from here we simplify and we get limit as X approaches infinity of the square, the vex squared times the squares of one plus one over x squared. And then from here we get limit as X approaches infinity of the squared of x squared, that's just X Times the square root of one plus one over x squared. Now evaluating at infinity we have infinity times the square of one plus one over infinity. And since constant over infinity Approaches zero, then 1 over infinity will also approach zero. And from here we have Infinity Times The Square The one which is just infinity. And so this is the value of the limits.