- #1

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[tex]

y = x + \sqrt{|x|}

[/tex]

Can I say that as x approaches infinity, y approaches x? That would mean that the function has an oblique asymptote at the line y=x but I'm not sure.

Thanks for any help!

- Thread starter flash
- Start date

- #1

- 68

- 0

[tex]

y = x + \sqrt{|x|}

[/tex]

Can I say that as x approaches infinity, y approaches x? That would mean that the function has an oblique asymptote at the line y=x but I'm not sure.

Thanks for any help!

- #2

- 12,117

- 154

y-x approaches zero as x approaches infinity.

Try subtracting x from both sides of your equation, and see whether the right-hand-side expression approaches zero or not.

Alternatively, you could plug in successively larger values of x into your expression (i.e, 100, then 1000, then 10,000).

Does the

Eg., for x = 100:

100 + sqrt(100) = ?

This number is ____ larger than 100.

Repeat for 1000, then 10,000.

- #3

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- #4

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It's likely that, if encountered in a physics or engineering application, you'd be completely justified in approximating the function simply by y=x for large x.

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