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★★★★☆ (4.5/5) Deducted 0.5 for lack of proofs and outdated visuals. calculus pauls notes
This is read as "the limit of f(x) as x approaches a is L". It means that as x gets arbitrarily close to a, f(x) gets arbitrarily close to L. Spend 10 minutes reading the upcoming topic on Paul’s site
| Course | Topics Covered | | :--- | :--- | | | Limits, Derivatives (product/quotient/chain rules, implicit differentiation, related rates), Applications of Derivatives (optimization, curve sketching, Mean Value Theorem), Introduction to Integrals (Riemann sums, Fundamental Theorem of Calculus, basic antiderivatives). | | Calculus II | Integration techniques (by parts, trig substitution, partial fractions), Improper integrals, Applications of integrals (area, volume, arc length), Sequences & Series (convergence tests, power series, Taylor/Maclaurin series), Parametric equations & Polar coordinates. | | Calculus III | 3D coordinate systems, Vector functions, Partial derivatives, Multiple integrals (double/triple), Line integrals, Green’s/Stokes/Divergence theorems (brief introduction). | This is read as "the limit of f(x) as x approaches a is L"
Find the limit of f(x) = 2x + 1 as x approaches 3.
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As x approaches 3, we can plug in values of x that are close to 3: