B.Sc Calculus Ch 3 (MV Theorem, Indet. Forms and Expansions) Notes

Calculus & Analytic Geometry (B.A / B.Sc.)

Chapter:03 (Mean Value Theorem, Indeterminate Forms, and Expansions)

In this chapter, we will study the following topics:

  • a theorem on differentiable functions
  • rolle’s theorem
  • michel rolle (a french mathematician)
  • proof of mean value theorem
  • strictly increasing function
  • partial derivative
  • find the value of c in mean value theorem
  • cauchy’s mean value theorem
  • generalized mean value theorem
  • cauchy’s form of the remainder after n terms
  • cauchy mean value theorem of order n
  • indeterminate forms
  • fundamental forms
  • algebraic, geometrical and trigonometric methods
  • rule of del hospital
  • successive applications of del hospital
  • another indeterminate form
  • compound indeterminate forms
  • gaussian binomial coefficient
  • Taylor and Maclaurin’s series
  • Maclaurin’s theorem
  • Bernoulli’s numbers
  • use of Leibnitz’s theorem
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