Squeeze Theorem: Statement, How to Use It and Examples
The squeeze (sandwich) theorem finds limits by trapping a function between two others. Step-by-step examples with x²·sin(1/x), sin(x)/x and cos(x)/x.
Tag: limits
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Limits at Infinity: Rules, Asymptotes and Examples
How to evaluate limits as x → ∞: divide by the highest power, the three degree rules for rational functions, growth rates, and radical examples.
L’Hôpital’s Rule: When and How to Use It (with Examples)
L’Hôpital’s rule evaluates 0/0 and ∞/∞ limits by differentiating top and bottom. Conditions, 6 worked examples, other indeterminate forms and common errors.
Limit of sin(x)/x as x → 0 Equals 1: Three Proofs
lim x→0 sin(x)/x = 1. See the squeeze theorem proof, the L’Hôpital shortcut (and why it’s circular), a numerical table and related limits.
Calculus Concepts Explained: The Core Ideas, Simply
The core calculus concepts explained simply: limits, continuity, derivatives, integrals, the Fundamental Theorem, series and multivariable ideas, with examples.