Limit definitions, standard limits, derivative as limit, basic differentiation rules.
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Q1 · Limits and Derivatives (Class 11 — ~20% weight) · EASY
Evaluate the limit: lim (x → 2) [(x² - 4)/(x - 2)]
Q2 · Limits and Derivatives (Class 11 — ~20% weight) · MEDIUM
If f(x) = x³ - 5x² + 7x - 3, find f'(2) using the first principle (definition of derivative).
Q3 · Limits and Derivatives (Class 11 — ~20% weight) · HARD
Evaluate: lim (x → 0) [(sin 3x · tan 2x)/(x²)]
Q4 · Limits and Derivatives (Class 11 — ~20% weight) · EASY
The derivative of f(x) = x³ + 5x² − 3x + 7 at x = 1 is: