What are common mistakes students make with limits?

1 Answer
Jim H
Apr 13, 2016

One common mistake is thinking that initial form 0/0 implies that the limit does not exist.

Explanation:

For example:

Evaluate lim_(xrarr2)(x^2-4)/(x^2-2x)

color(red)"Student Error"
lim_(xrarr2)(x^2-4)/(x^2-2x) = ((2)^2-4)/((2)^2-2(2)) = 0/0 = color(red)( DNE)

color(blue)"Correct solution"

lim_(xrarr2)(x^2-4)/(x^2-2x) = lim_(xrarr2)((x+2)cancel((x-2)))/(xcancel((x-2))) = 4/2 = 2

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