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Introductory calculus : maxima, minima, and special functions /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York [New York] (222 East 46th Street, New York, NY 10017) :
Momentum Press,
2015.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 1. Increasing and decreasing functions and extrema
- Some terminology
- The derivative test for monotonicity and extrema
- The proof of Fermat's theorem.
- 2. Understanding the mean value theorem
- Rolle's theorem and the mean value theorem.
- 3. Determining concavity and extrema
- The second derivative and extrema
- The proof of the second derivative test for local extrema.
- 4. Drawing the graph of a function.
- 5. Using maxima and minima in real applications
- Optimization
- Applications to economics.
- 6. The importance of inverse functions
- Inverse trigonometric functions.
- 7. Using the derivative of an inverse function
- The general expression
- The derivatives of inverse trigonometric functions
- The proof of theorem 1 (optional).
- 8. Applying the natural exponential function and the natural logarithm
- The natural logarithm.
- 9. Exponential functions with arbitrary bases
- Logarithmic functions with arbitrary bases
- Arbitrary powers of x.
- 10. Orders of magnitude in exponential functions
- Logarithmic growth
- The natural exponential function as a limit of polynomials.
- 11. Using exponential functions in growth and decay rates
- The solution of the differential equation y = ky
- Compound interest.
- 12. Introduction to hyperbolic and inverse
- Hyperbolic functions
- Inverse hyperbolic functions.
- 13. Using L'Hopital's rule for indeterminate forms
- The indeterminate form 0/0
- The indeterminate form [infinity] / [infinity]
- The indeterminate form 0 / [infinity]
- The indeterminate forms 1[infinity], [infinity]0 and 00
- The indeterminate form [infinity]
- [infinity].