Sweet and Sour Limits | Robert Low

Eagle-eyed friend of the blog @robjlow spotted an error in Uncle Colin’s last answer. As I’m forever telling my students, making errors is how you learn; Rob has graciously delivered a lesson for us all. Thanks for keeping me honest!

Recently, Uncle Colin gave a couple of ways to see that

\[ \lim_{x \to \infty} \left\{ \sqrt{x^2 + 3x} – x\right\} = \frac{3}{2} \]

One approach, the sweet, used the binomial theorem, to write

\[ \sqrt{x^2 + 3x} = x\sqrt{1+\frac{3}{x}} \approx x\left(1+\frac{3}{2x}\right). \]

The very suspicious minded mind be a little hesitant, because the error in…

Continue reading at:
http://ift.tt/2ohN9Kr

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s