High School Calculus/Infinite Limits

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The limit as x approaches gives you the horizontal asymptote.

\lim_{x \to -\infty}x

\lim_{x \to \infty}x = L

You can use L'Hopital rule to help you with these limits

f(x)=\lim_{x \to \infty}\frac{2x}{2x^2}

f(x)=\frac{\infty}{\infty}

This is an indeterminate form so you can use L'Hopital's rule.

To do this you need to take \frac{f \prime (x)}{g \prime (x)}

From this you get

\lim_{x \to \infty}\frac{2}{4x}

This gives you

\frac{2}{\infty}

This is no longer in indeterminate form so, we get

L=0