lightbulb Key Concepts

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1. Concept of a Limit

A limit exists when the values of a function f(x) approach a specific value L as x approaches a value 'a' from both sides.

2. L'Hopital's Rule

If the limit results in an indeterminate form (0/0 or ∞/∞), the limit can be found by differentiating the numerator and denominator separately.

3. Standard Limits

• lim (x→0) sin x / x = 1
• lim (x→0) (eˣ - 1) / x = 1
• lim (x→0) log(1+x) / x = 1
• lim (x→a) (xⁿ - aⁿ) / (x - a) = naⁿ⁻¹