Unit: Analytical Application of Differentiation Chapter: Mean & Extreme Value Theorem Reference: – Rolle’s Theorem, Intermediate value theorem, Extreme values, Critical points, Local extrema, Absolute extrema, closed intervals, First & Second derivative test, Concavity, Inflection points, Approximate values, Mean value theorem for integrals, Average value functions. After studying this chapter, you should be able […]
Unit: Limits & Continuity Chapter: Definition & Properties of Limits Reference: – Limit laws, Epsilon-delta notation, Algebraic properties of limits, Limits functions, Continuous & Discontinuous limits, Infinite & Asymptote limits, Intermediate value theorem, L-Hospital Rule, Squeeze theorem, Exponential limits, Logarithmic limits, Concept of limits, Behaviour of limits After studying this chapter, you should be […]
Unit: Limits & Continuity Chapter: Continuity of a Function & Domain Reference: – Jump & Infinite Continuous function, Interval of continuity, Continuity & Limits, Piecewise functions, Domain Restrictions, Infinite & Asymptote limits, Uniform Continuity, Common Functions, Vertical Asymptotes, Exponential limits, Logarithmic limits, Hole in the domain, Behaviour of functions & Domain After studying this […]
Unit: Limits & Continuity Chapter: Asymptote, Squeeze & Intermediate value theorem Reference: – Behaviour of a function, Different types of Asymptotes, Continuity of a function, Piecewise functions, Existence of Root Methods, Infinite & Asymptote limits, Bisection methods, Oblique Functions, Vertical Asymptotes, Exponential functions, Logarithmic limits, Squeeze theorem, Intermediate value theorem, Rational Functions After studying this […]
Unit: Differentiation-Fundamental Properties Chapter: Derivation of a Function Reference: – Derivative, Rate of change, Tangent line, Instantaneous rate of change, Slope of a line, Higher order derivatives, Differentiability, Chain rule, Product rule, Quotient rule, Dependent variables, Properties of a function, Curvature, Growth & Decay After studying this chapter, you should be able to: Basic Concept […]
Unit: Differentiation-Fundamental Properties Chapter: Continuity & Differentiability Reference: – Continuous, Discontinuous, Point of Discontinuity, Removable Discontinuity, jump discontinuity, Tangent line, Differentiation, Derivatives, Cusp, Critical point, Piecewise function, Continuity implication, Types of continuity & Differentiability, Mixed properties, Rules & Formation. After studying this chapter, you should be able to: Fundamental Properties of Continuous Function. Continuities […]
Unit: Differentiation-Fundamental Properties Chapter: Elementary Functions Reference: – Elementary Functions, Polynomial Functions, Exponential functions, Logarithmic functions, Power rules, Trigonometric functions, Composite functions, Chain rules, Quotient rules, Inverse functions, Rational functions, Domain & Range, Absolute value functions. After studying this chapter, you should be able to: Introduction & Basic rules. Types & Application of Elementary Function. […]
Unit: Differentiation-Composite, Implicit & Inverse function Chapter: Chain Rule for Composite Functions Reference: – Composite Functions, Differentiation of composite functions, Chain rule, Power functions, Exponential functions, Logarithmic functions, Hyperbolic functions, Implicit, Multiple compositions, Parametric equations, Higher Dimensions, Partial Derivatives. After studying this chapter, you should be able to: Composite functions & its Differentiation. Nested function […]
Unit: Differentiation-Composite, Implicit & Inverse function Chapter: Implicit Differentiation Reference: – Implicit Functions, Implicit equations, Derivatives of Implicit relations, Chain rules, Slope of tangent lines, Equation of tangent line, Implicit differentiation, Higher order derivatives, vertical & Horizontal Tangent lines, Curve sketching, Optimization, Trigonometric Functions. After studying this chapter, you should be able to: Differentiation Rule […]
Unit: Differentiation-Composite, Implicit & Inverse function Chapter: General Inverse Functions Reference: -Inverse functions, One to-one functions, Invertibility, Inverse algebraically, Graphing the inverse functions, Equations & Graphs, Composition of inverse functions, Domain & Range of Inverse functions, Derivatives of Inverse functions, Applications & Properties. After studying this chapter, you should be able to: Introduction & Verification […]