What are common mistakes students make with limits?

1 Answer
Apr 13, 2016

Answer:

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#