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

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Answer 1 · 2018-06-10T21:36:43

The limit $x -> oo, f(x) -> oo$

As $x$ approaches infinity the +1 will lose all significance so we can just consider:

$x(sqrt(x^2))= x(x)= x^2$

we know $x -> oo, x^2 -> oo$ so we can conclude:

$f(x) = x(sqrt(x^(2)+1))$

The limit $x -> oo, f(x) -> oo$

Answer 2 · 2018-06-10T21:38:19

$lim_(x to oo) x(sqrt(underbrace(x^(2))_("humungous")+underbrace(1)\_("just 1")))$

$= lim_(x to oo) x* underbrace(sqrt(x^2))_("a positive number")$

$= lim_(x to oo) x^2 = oo$

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