Question

What are common mistakes students make with limits?

Answer 1

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`