21. The Generalized Mean Value Theorem (Cauchy's MVT), L' Hospital's Rule, and their Applications

  1. Ulrich L. Rohde1,2,
  2. G. C. Jain3,
  3. Ajay K. Poddar2 and
  4. A. K. Ghosh4

Published Online: 28 DEC 2011

DOI: 10.1002/9781118130155.ch21

Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners

Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners

How to Cite

Rohde, U. L., Jain, G. C., Poddar, A. K. and Ghosh, A. K. (2011) The Generalized Mean Value Theorem (Cauchy's MVT), L' Hospital's Rule, and their Applications, in Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118130155.ch21

Author Information

  1. 1

    BTU Cottbus, Germany

  2. 2

    Synergy Microwave Corporation, Paterson, NJ, USA

  3. 3

    Defense Research & Development Organization, Maharashtra, India

  4. 4

    Department of Aerospace Engineering, Indian Institute of Technology – Kanpur, Kanpur, India

Publication History

  1. Published Online: 28 DEC 2011
  2. Published Print: 9 DEC 2011

ISBN Information

Print ISBN: 9781118117750

Online ISBN: 9781118130155

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Keywords:

  • generalized mean value theorem (Cauchy's MVT);
  • indeterminate forms, L'Hospital's rule, ratio of derivatives to infinity;
  • limit of a ratio of functions f(x), g(x) approaching infinity

Summary

This chapter contains sections titled:

  • Introduction

  • Generalized Mean Value Theorem (Cauchy's MVT)

  • Indeterminate Forms and L'Hospital's Rule

  • L'Hospital's Rule (First Form)

  • L'Hospital's Theorem (For Evaluating Limits(s) of the Indeterminate Form 0/0.)

  • Evaluating Indeterminate Form of the Type ∞/∞

  • Most General Statement of L'Hospital's Theorem

  • Meaning of Indeterminate Forms

  • Finding Limits Involving Various Indeterminate Forms (by Expressing them to the Form 0/0 or ∞/∞)