# To Accumulate a Rate — Integrate!

Teaching High School Mathematics

# Algebra Errors in Calculus

I just took this picture on my patio and thought…”wouldn’t it be fun to have students bring chalk one day and do math in the parking lot?”

Three error’s from my first Calculus assessment.

1. $x^{2}-x=\left( x-1\right) \left( x+1\right)$

2. $\dfrac {2x} {x\left( x-1\right) }=\dfrac {x} {x-1}$
Multiple students did this to my surprise and showed canceling the 2 in the numerator with the x in the denominator. (Look at the pic above.) Usually I can see the mistakes that are going to happen, but this was a new one for me.

3. This one is my favorite. Talk about a coincidence.
$\lim _{x\rightarrow \infty }\dfrac {x^{2}-2x+1} {4x^{2}}=\dfrac {1} {4}$
$\lim _{x\rightarrow \infty }\dfrac {-2x+1} {4}$ Yes they cancelled the $x^2$‘s.
And then… $\dfrac {-2\left( 0\right) +1} {4}=\dfrac {1} {4}$
I still can’t believe it. I can’t plug in infinity, so how about zero?

### One comment on “Algebra Errors in Calculus”

1. About number 2 I understand that the mistake comes from the same exercise with x^2 when “2 is cancelled” whith x.

I tell them to verbalise the properties in the right way.

Great blog btw.

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This entry was posted on September 23, 2012 by in Uncategorized.