Category: Calculus

1. Limit Exercises Exo 1: Basic Limit Calculation Problem: \[ \lim_{x \to 0} \frac{\sin(x)}{x} \] Solution: This is a standard limit which is part of the limit formulas: \[ \lim_{x \to 0} \frac{\sin(x)}{x} = 1 \] Exo 2: Using L’Hopital’s Rule Problem: \[ \lim_{x \to 0} \frac{1 – \cos(x)}{x} \] Solution: This is a \(\frac{0}{0}\) […]

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Basic Calculus Formulas: Limits: \(\lim_{x \to a} f(x) = L\), where \(f(x)\) approaches \(L\) as \(x\) approaches \(a\). \(\lim_{x \to a} \frac{f(x) – f(a)}{x – a} = f'(a)\) (Definition of the derivative). \(\lim_{x \to 0} \frac{\sin(x)}{x} = 1\). \(\lim_{x \to 0} \frac{1 – \cos(x)}{x} = 0\). Derivative Formulas: Power Rule: \(\frac{d}{dx}[x^n] = n x^{n-1}\). Constant […]

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