Question

I'm evaluating an infinite limit and this is how far I got. Limit as x approaches 2 from the left (x^2-6x+5)/(x-2) and I simplified the top polynomial to (x-1)(x-5)/(x-2) and I know x<2 but i get (0)(-4)/(-1), is that - infinity?

Answer 1

nope it should be positive infinity. as x approaches to 2 from the left, the denominator remains negative but |x-2| -> 0 as x -> 2^-, i.e. the distance between x = 2 and x as x goes to 2 becomes infinitely small but remains negative. Now the numerator as x approaches 2 always remains negative as well. Since both numerator/denominator are negative near 2 from the left, the limit is positive infinity, i.e limit does not exist.