Monomath – CBSE | GSEB | IB | JEE Maths by Ajay Yadav (Math King of Katargam) – 15+ Years Experience. Study Notes, Video Lessons, Formula Sheets & PYQs.
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Continuity and Differentiability

Previous Year Questions (2022-2024)

📅 Year 2022

  1. Find k if f(x) = {kx+1, xπ} is continuous at x=π.
    Show Solution
    LHL = limx→π^- (kx+1) = kπ+1\nRHL = limx→π^+ cos x = -1\nf(π) = kπ+1\nkπ+1 = -1 => kπ = -2 => k = -2/π
  2. Find dy/dx if x2 + y2 = 25.
    Show Solution
    Differentiating: 2x + 2ydydx = 0\ndydx = -xy

📅 Year 2023

  1. Find k if f(x) = {kx+1, xπ} is continuous at x=π.
    Show Solution
    LHL = limx→π^- (kx+1) = kπ+1\nRHL = limx→π^+ cos x = -1\nf(π) = kπ+1\nkπ+1 = -1 => kπ = -2 => k = -2/π
  2. Find dy/dx if x2 + y2 = 25.
    Show Solution
    Differentiating: 2x + 2ydydx = 0\ndydx = -xy

📅 Year 2024

  1. Find k if f(x) = {kx+1, xπ} is continuous at x=π.
    Show Solution
    LHL = limx→π^- (kx+1) = kπ+1\nRHL = limx→π^+ cos x = -1\nf(π) = kπ+1\nkπ+1 = -1 => kπ = -2 => k = -2/π
  2. Find dy/dx if x2 + y2 = 25.
    Show Solution
    Differentiating: 2x + 2ydydx = 0\ndydx = -xy