Continuity and Differentiability

⭐ Important Questions

1. Find k if f(x) = {kx+1, xπ} is continuous at x=π.
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   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.
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   Differentiating: 2x + 2ydydx = 0\ndydx = -xy