- #1

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## Homework Statement

Lim as x goes to infinity of sqrt(x^2 + 1) / x

## The Attempt at a Solution

know you are supposed to divide by the highest power of x, but how does that work when you have an x^2 within a sqrt?

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- Thread starter icosane
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- #1

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Lim as x goes to infinity of sqrt(x^2 + 1) / x

know you are supposed to divide by the highest power of x, but how does that work when you have an x^2 within a sqrt?

- #2

danago

Gold Member

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Try writing x^{2}+1 as x^{2}(1+1/x^{2}).

See if that helps.

See if that helps.

- #3

HallsofIvy

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And remember that [itex](1/x)\sqrt{x^2+ 1}= \sqrt{(1/x^2)(x^2+ 1}[/itex]

- #4

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limit x--->infinity sqrt(1+1/X^2)

and when x goes to infinity 1/X^2 goes to zero

so your final limit will go to 1

hope you got it!!!!!!!!!!!!

- #5

HallsofIvy

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You've got three responses saying the same thing in different ways!

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