∫ Calculus I

Number sets, functions, limits, continuity, derivatives, integrals, series and differential equations. Every topic with step-by-step theory, worked examples and solved exercises.

📋 Formulario

Complete Theory

Worked Examples

Example 1Complete analysis of f(x)=xe−xf(x)=xe^{-x}
Example 2Complete analysis of f(x)=x2x2−1f(x)=\dfrac{x^2}{x^2-1}

Exercises with Solutions

Exercise 1Function analysis — cubic polynomialMedium
📋 Problem to solve
Fully analyze f(x)=x3−3xf(x)=x^3-3x and find maxima, minima, inflection points.
Exercise 2Function analysis — rational functionHard
📋 Problem to solve
Fully analyze f(x)=x−1x+1f(x)=\dfrac{x-1}{x+1}.
Exercise 3Function analysis — logarithmHard
📋 Problem to solve
Fully analyze f(x)=x−ln⁡xf(x)=x-\ln x.
Exercise 4Function analysis — oblique asymptoteVery Hard
📋 Problem to solve
Fully analyze f(x)=xe1/xf(x)=xe^{1/x}.
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Recommended Books

Introductory
Calculus: Early Transcendentals
Stewart, Clegg, Watson
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