Worked examples

Differential calculus and Taylor

One sheet for each type of problem, with several worked examples of increasing difficulty: first the computation, then the explanation in words. Each sheet starts with links to the theory it uses.

• 1Derivatives using the definition
• 2Derivatives of composite functions
• 3Tangent lines
• 4Differentiability of piecewise functions and functions with absolute value
• 5Applications of Lagrange's theorem and monotonicity
• 6Limits with L'Hôpital's rule
• 7Limits with Taylor's formula
• 8Taylor expansions of composite functions and estimates with the Lagrange remainder