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Calculus
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LIMITS
The limit concept
Limit definition and intuition
Properties of limits
Special limits
Zero denominator limits
Infinite limits and limits involving infinity
Left-hand and right-hand limits
Continuity
Definition of continuity
Properties of continuity
Intermediate Value Theorem (IVT)
II DIFFERENTIATION
Definition of the derivative and derivatives of some simple functions
Definition of the derivative
Derivative of a constant function
Derivative of a linear function
Derivative of a power function
Numerical derivatives
Rules of differentiation
Constant multiple of a function rule
Rule for sums and differences
Product rule
Quotient rule
Chain rule
Implicit differentiation
Additional derivatives
Derivative of the natural exponential function ex
Derivative of the natural logarithmic function ln x
Derivatives of exponential functions for bases other thane
Derivatives of logarithmic functions for bases other thane
Derivatives of trigonometric functions
Derivatives of inverse trigonometric functions
Higher-order derivatives
INTEGRATION
7. Indefinite integral and basic integration formulas and rules
Antiderivatives and the indefinite integral
Integration of constant functions
Integration of power functions
Integration of exponential functions
Integration of derivatives of trigonometric functions
Integration of derivatives of inverse trigonometric functions
Two useful integration rules
8. Basic integration techniques
Integration by substitution
Integration by parts
Integration by using tables of integral formulas
9. The definite integral
Definition of the definite integral and the First Fundamental Theorem of Calculus
Useful properties of the definite integral
Second Fundamental Theorem of Calculus
Mean Value Theorem for Integrals
APPLICATIONS OF THE DERIVATIVE AND THE DEFINITE INTEGRAL
Applications of the derivative
Slope of the tangent line at a point
Instantaneous rate of change
Differentiability and continuity
Increasing and decreasing functions, extrema, and critical points
Concavity and points of inflection
Mean Value Theorem
Applications of the definite integral
Area of a region under one curve
Area of a region between two curves
Length of an arc
Appendix A: Basic functions and their graphs
Appendix B: Basic differentiation formulas and rules
Appendix C: Integral formulas
Answer key
Worked solutions
IITJEE Books
Calculus
Mathematics
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