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Continuity and Differentiability

Previous Year Questions (2022-2024)

📅 Year 2022

  1. Check continuity of f(x) = {x2 sin(1/x), x≠0; 0, x=0} at x=0.
    Show Solution
    limx→0 x2 sin(1/x) = 0 (squeeze theorem, since -x2 <= x2 sin(1/x) continuous.
  2. Find k if f(x) = {kx2, x2} is continuous at x=2.
    Show Solution
    LHL = limx→2^- kx2 = 4k\nRHL = limx→2^+ 3 = 3\nf(2) = 4k\nFor continuity: 4k = 3 => k = 3/4

📅 Year 2023

  1. Check continuity of f(x) = {x2 sin(1/x), x≠0; 0, x=0} at x=0.
    Show Solution
    limx→0 x2 sin(1/x) = 0 (squeeze theorem, since -x2 <= x2 sin(1/x) continuous.
  2. Find k if f(x) = {kx2, x2} is continuous at x=2.
    Show Solution
    LHL = limx→2^- kx2 = 4k\nRHL = limx→2^+ 3 = 3\nf(2) = 4k\nFor continuity: 4k = 3 => k = 3/4

📅 Year 2024

  1. Check continuity of f(x) = {x2 sin(1/x), x≠0; 0, x=0} at x=0.
    Show Solution
    limx→0 x2 sin(1/x) = 0 (squeeze theorem, since -x2 <= x2 sin(1/x) continuous.
  2. Find k if f(x) = {kx2, x2} is continuous at x=2.
    Show Solution
    LHL = limx→2^- kx2 = 4k\nRHL = limx→2^+ 3 = 3\nf(2) = 4k\nFor continuity: 4k = 3 => k = 3/4