The value of $\lim_{x \to \infty} (1 + x^2)e^{-x}$ is

Calculus in GATE CS tests single-variable differential and integral calculus, foundational limit evaluations, continuity and differentiability of piecewise/absolute-value functions, and mean value theorems (Rolle's and LMVT). Earlier years (2012-2015) also included numerical methods such as Newton-Raphson, Bisection, and Trapezoidal/Simpson's rules, whereas recent papers (2020-2026) focus heavily on analytical properties: odd/even symmetry in single and multiple integrals, boundary extrema, points of non-differentiability, and MSQ-based structural analyses of functions.