← Back to Test

Problem 1 - Entrance Test

Evaluate the limit: lim (x→0) (e^(x^2) - cos(x)) / x^2

Correct: C

Using L'Hopital's Rule twice: First derivative: (2xe^(x^2) + sin(x)) / 2x. Second derivative: (2e^(x^2) + 4x^2e^(x^2) + cos(x)) / 2. Evaluating at x=0 gives (2 + 1) / 2 = 3/2.