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## Homework Statement

lim [√(2x

^{2}+1)]/(3x - 5)

x→-∞

I know that the answer is -√2/3. That is the answer my professor had on this example, and the math lab tutor also agreed, and so did my graphing calculator. But I keep getting √2/3 on paper. The math lab tutor explained yesterday why it is negative to me, but I didn't write it down, as I wanted to ask a few more questions, so I forgot why, which has left me irritated that I forgot.

## Homework Equations

## The Attempt at a Solution

lim [√(2x

^{2}+1)]/(3x - 5)

x→-∞

lim √(2x

^{2}/x

^{2}+1/x

^{2})

x→-∞

/

(3x/x - 5/x)

lim √2 + 0

x→-∞

/

3 - 0

√2/3

The professor said something about the numerator being +∞ and the denominator being -∞, so the answer must be negative, but I thought the limit of the denominator was 3, which is positive?

Thanks for any help!