## Differential CalculusDifferential Calculus, An Outgrowth Of The Problems Concerned With Slope Of Curved Lines And The Areas Enclosed By Them Has Developed So Much That Texts Are Required Which May Lead The Students Directly To The Heart Of The Subject And Prepare Them For Challenges Of The Field. The Present Book Is An Attempt In This Regard. An Excellent Book On Differential Calculus This Book Has Been Meticulously Planned And Numerous Solved Examples Have Been Selected To Make The Subject Interesting; Besides Problems Are Given At The End Of Each Main Theorem Which Supplement The Text And By Solving Them The Reader Can Judge His Level Of Understanding Of The Given Facts.Exercises Have Been Framed By Arranging Questions In Such A Manner That After Doing Illustrative Examples, One Should Not Feel Difficulty In Solving Any Problem. Considerable Material Has Been Included Here That Covers A Large Number Of Courses. This Has Been Done To Make The Book More Flexible, To Provide A Useful Book Of Reference And To Stimulate Further Interest In The Topics. |

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Very helpful and simplified book .

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save this one until you have not yet bought your own textbook,

### Contents

REAL NUMBERS | 1 |

CONTINUITY | 27 |

DIFFERENTIABILITY | 48 |

SUCCESSIVE DIFFERENTIATION | 60 |

ROLLES THEOREM MEAN VALUE | 82 |

INDETERMINATE FORMS | 106 |

3 | 114 |

The forms 0 1 and | 121 |

PARTIAL DIFFERENTIATION | 128 |

TANGENTS AND NORMALS | 175 |

CURVATURE | 229 |

ENVELOPES AND EVOLUTES | 265 |

ASYMPTOTES | 286 |

MULTIPLE POINTS | 321 |

CURVE TRACING | 346 |

### Common terms and phrases

angle asymptote parallel centre of curvature chord of curvature closed interval co-ordinates concave conjugate point constant continuous cos2 cosec cosh cusp derivative differential coefficient discontinuity double point dx dy dy dx ellipse equated to zero equation of curve equation of tangent equiangular spiral Euler's theorem Example 1 Find Exercise family of curves Find the asymptotes Find the envelope find the value finite following curves function/(x given curve given equation Hence homogeneous function Illustrative Examples Example indeterminate forms infinite Jacobian Let us consider lowest degree terms mean value theorem negative normal obtained by equating origin parabola parallel to x-axis parameter pedal equation perpendicular points of inflexion positive number prove radius of curvature radius vector rational numbers real numbers respect Rolle's theorem Show Similarly sin2 straight line Substituting subtangent Taylor's theorem y-axis