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GATE Engineering Mathematics: Calculus: Limits, continuity, mean value theorems, maxima and minima, Taylor series – Previous Year Questions

6 GATE previous year questions on Calculus: Limits, continuity, mean value theorems, maxima and minima, Taylor series (Engineering Mathematics, Civil Engineering) with answers and explanations, from every paper.

  1. GATE 2023 CE (CE1) Q48 (2 marks, Multiple select) – For the function f(x) = ex x ; x R, which of the following statements is/are TRUE?
  2. GATE 2024 CE (CE2) Q14 (1 mark, Multiple choice) – The function f(x) = x3 - 27x + 4, 1 x 6 has
  3. GATE 2025 CE (CE2) Q44 (2 marks, Multiple select) – Consider the function given below and pick one or more CORRECT statement(s) from the following choices. f(x) = x3 - 152x2 + 18x + 20
  4. GATE 2025 CE (CE1) Q36 (2 marks, Multiple choice) – The value of x (x - x2 + x) is equal to
  5. GATE 2025 CE (CE1) Q48 (2 marks, Numerical answer) – The maximum value of the function h(x) = -x3 + 2x2 in the interval [-1, 1.5] is equal to (*rounded off to 1 decimal place*).
  6. GATE 2026 CE (CE2) Q36 (2 marks, Multiple choice) – Let f(x) = vmatrix x3 & x & x \\ 6 & -1 & 0 \\ p & p2 & p3 vmatrix where p is a constant. The value of d3dx3 f(x) at x = 0 is