Trap 1: Degree confusion in x -> -infinity lim(x->-infinity) sqrt(x^2 + x) + x. Students write sqrt(x^2) = x. Wrong! For x < 0, sqrt(x^2) = -x. Correct: sqrt(x^2 + x) = |x| * sqrt(1 + 1/x) = -x * sqrt(1 + 1/x) when x < 0. Then expression = -x * sqrt(1 + 1/x) + x = x(-sqrt(1+1/x) + 1). As x -> -infinity, this -> -infinity * 0, need careful expansion. Using conjugate: answer = -1/2.

Trap 2: sin(x)/x when x is in degrees lim(x->0) sin(x degrees)/x = sin(pi*x/180)/(x) -> pi/180, NOT 1.

Trap 3: [sin x / x] as x -> 0 sin x / x -> 1 from below (for small x > 0, sin x < x). So [sin x / x] = 0 near 0, not 1.

Trap 4: Misapplying L'Hopital lim(x->0) (sin x)/x is 1 by standard limits. Using L'Hopital: cos(0)/1 = 1. Both work, but don't use L'Hopital on lim(x->0) (x * sin(1/x)) — this is NOT 0/0 form, it's 0 * bounded.

Trap 5: Canceling before checking lim(x->1) (x^2-1)/(x-1) = lim (x+1) = 2. Correct. But only valid because we cancel (x-1) and then substitute. Don't substitute x=1 before canceling.