Trap 1: Radians vs Degrees The limit sin$\frac{x}{x}$ = 1 ONLY when x is in radians. If x is in degrees, the limit is pi/180. JEE occasionally tests this distinction.

Trap 2: sqrt($x^2$) = |x|, NOT x When x < 0, sqrt($x^2$) = -x. This is critical for limits as x -> -infinity. For example, lim(x->-inf) sqrt($x^{2+3x}$)+x: since x < 0, sqrt($x^2$) = -x, not x.

Trap 3: Greatest Integer Function Traps lim(x->0) [sin x/x] = 0, not 1. Since sin$\frac{x}{x}$ < 1 for small x, the floor function gives 0. Similarly, for x in (-1, 0), [x] = -1 (not 0).

Trap 4: Misapplying L'Hopital's Rule L'Hopital only works for 0/0 and infinity/infinity. Don't apply it to non-indeterminate forms. Don't use the quotient rule — differentiate numerator and denominator separately.

Trap 5: 1^infinity is NOT equal to 1 Many students assume 1^anything = 1. This is false for the 1^infinity form. Always use the exponential formula.

Trap 6: Continuity vs Differentiability f(x) = |x| is continuous at 0 but not differentiable. f(x) = x*sin$\frac{1}{x}$ (with f(0)=0) is continuous at 0 but not differentiable. Continuity does NOT imply differentiability.

Trap 7: One-sided behavior of e^$\frac{1}{x}$ As x -> 0+, e^$\frac{1}{x}$ -> infinity. As x -> 0-, e^$\frac{1}{x}$ -> 0. This asymmetry is heavily tested.

Trap 8: Fractional Part near integers {x} approaches 1 from the left of any integer, but {n} = 0. Don't assume {x} -> 0 from both sides near an integer.