What is the limit of $[sqrt(x^2+1)] / x$ as x approaches infinity?

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Answer 1 · 2016-07-01T05:38:27

$1$

So, you have $sqrt(x^2+1)/x$

As $x$ approached infinity, any constant such as the $1$ here can be ignored because it is infintesimally small. Now you have

$sqrt(x^2)/x$

This is equal to

$x/x$

which is equal to $1$

What is the limit of [sqrt(x^2+1)] / x [sqrt(x^2+1)] / x as x approaches infinity?