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Indeterminate Form

149.00

This module is designed to introduce the various indeterminate forms and evaluation using the Maclaurin definition and L-Hospital rule (both methods compared to evaluate relative degree of difficulty/ease). Significant number of model questions paper problems have been solved to give a comprehensive understanding of the examiner’s perspective.

Salient features of this module are: 

  • Pre-requisites to Elements of Differential Calculus
  • Graphical visualization 
  • Concept testing 
  • Unravelling examiners mind 
  • Model question paper 

Course Contents: 

Pre-requisites to Elements of Differential Calculus

  • Sign of Trigonometric Identities
    • Sign of Trigonometric Identities – Introduction
    • Sign of Trigonometric Identities – Quad I
    • Sign of Trigonometric Identities – Quad II
    • Sign of Trigonometric Identities – Quad III
    • Sign of Trigonometric Identities – Quad IV
    • Sign of Trigonometric Identities – Summary
    • Sign of Trigonometric Identities – 1
    • Sign of Trigonometric Identities – 2
  • General solution for Trigonometric  ratios
    • General solution for Trigonometric ratios (Example 1)
    • General solution for Trigonometric ratios (Example 2)
    • General solution for Trigonometric ratios (Example 3)
    • General solution for Trigonometric ratios (Example 4)
  • Concept of derivate – Slope
    • Concept of Derivative – Slope – Straight line
    • Concept of Derivative – Slope – Curve
  • Differentiation of Basic functions
    • Introduction – Chain and Quotient Rules
    • Derivative of tan x
    • Derivative of sec x
    • Derivative of cosec x
    • Derivative of cot x
    • Derivative of [y = e^x * x^n]
    • Derivative of [y = tan^(-1) x
    • Derivative of [y = x/(ax+b)] – Quotient rule
    • Derivative of [y = x/(ax+b)] – Chain rule
    • Derivative of [x^2 + y^2 = k]
    • Derivative of [y = 1/sqrt(ax^2 +b)]
    • Derivative of [y = a^x (log (1+x^2))]
    • Derivative of [y = a^sinx (1+sin^2 (x)) sec x]
    • Graphical understanding of trigonometric derivatives
  • Application of Derivative
    • Finding nature of the curve
    • Interpreting curvature of a curve
    • Linearization of a curve
    • L-Hospital Rule
    • Use of second derivative (curvature)
    • Maxima & Minima – 1
    • Maxima & Minima – 2
  • Angle between Curves & Radius of curvature
    • Essential trigonometric identities 1
    • Essential trigonometric identities 2
    • Essential trigonometric identities 3
    • Essential trigonometric identities 4
    • Essential trigonometric identities 5

INDERTERMINATE FORM: 

  • Indeterminate Forms – (Understanding L-Hospital Rule)
    • Understanding L-Hospital Rule
  • Indeterminate Forms – Problems
    • Problem 1
    • Problem 2
    • Problem 3
    • Problem 4
    • Problem 5
    • Problem 5 (Alternate Method)
    • Problem 6
    • Problem 7
    • Problem 8

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