1. Explain what's wrong with the following solution, and provide a correct solution to the question. Question. Find limx0 x2 + 3x 4 x2 2x + 3 . Solution. We can use the idea of higher power domination and throw away terms with lower powers. So the limit is equivalent to limx0 x2 x2 = limx0 1 = 1.

2. Explain what's wrong with the following solution, and provide a correct solution to the question. Question. Find limx x2 + 2x 2x2 + 6 Solution. We have limx(x2 + 2x) = , limx(2x2 + 6) = , so limx x2 + 2x 2x2 + 6 = = 1.