The GATE Grind

GATE Calculus and Optimization: Limits, continuity and differentiability – Previous Year Questions

7 GATE previous year questions on Limits, continuity and differentiability (Calculus and Optimization, Data Science and Artificial Intelligence) with answers and explanations, from every paper.

  1. GATE 2024 DA Q33 (1 mark, Numerical answer) – Let f: R R be the function f(x) = 11 + e-x. The value of the derivative of f at x where f(x) = 0.4 is (rounded off to two decimal places).
  2. GATE 2024 DA Q37 (2 marks, Multiple choice) – Let f: R R be a function. f(x) = cases -x, & if x < -2 \\ ax2 + bx + c, & if x [-2, 2] \\ x, & if x > 2 cases Which ONE of the following choices gives…
  3. GATE 2024 DA Q60 (2 marks, Numerical answer) – Evaluate the following limit: x 0((x2 + 1) x)x2 = .
  4. GATE 2025 DA Q24 (1 mark, Multiple select) – Consider two functions f: R R and g: R (1, ). Both functions are differentiable at a point c. Which of the following functions is/are ALWAYS…
  5. GATE 2025 DA Q32 (1 mark, Numerical answer) – t +t2 + t - t = (*Round off to one decimal place*)
  6. GATE 2025 DA Q59 (2 marks, Numerical answer) – Let f: R R be such that f(x) - f(y) (x - y)2 for all x, y R. Then f(1) - f(0) = (*Answer in integer*)
  7. GATE 2026 DA Q35 (1 mark, Numerical answer) – The value of i=0 j=1 2-i\,3-j is . (*Answer in integer*)