Solved Problems Contents - A
     The limit of a function
     Continuous function
     Limits at infinity (or limits of functions as x approaches positive or negative infinity)
        Vertical asymptote
        Horizontal asymptote
        Slant or oblique asymptote
     Limits of functions properties
        Limits of functions properties use
     Limits of rational functions
        Evaluating the limit of a rational function at infinity
        Evaluating the limit of a rational function at a point
        The limit of a rational function that is defined at the given point
        The limit of a rational function that is not defined at the given point
     The limit of a rational function at infinity containing roots (irrational expressions)
        The limit of a rational function at a point containing irrational expressions, use of substitution
     Evaluating trigonometric limits
     Evaluating limits of functions based on the definition of the natural number e
     Use of the composition rule to evaluate limits of functions
     Differential calculus, derivatives and differentials
     The derivative of a function
        Definition of the derivative of a function
     The equation of the line tangent to the given curve at the given point
     Determining the derivative of a function as the limit of the difference quotient
     Determining the lines tangent to the graph of a function from a point outside the function
     Derivatives of functions
        The quotient rule
        Differentiation using the chain rule
        Table of derivatives of elementary functions
        Differentiation rules
     The chain rule applications
        Implicit differentiation
     Generalized power rule
     Logarithmic differentiation
        Derivative of a composite exponential function
        Use of the logarithmic differentiation
     Derivative of the inverse function
     Derivative of parametric functions, parametric derivatives
     Applications of the derivative
     Tangent, normal subtangent and subnormal
        Properties of the parabola
        Property of power functions
        Property of exponential functions
     Angle between two curves
     Differential of a function
        Use of differential to approximate the value of a function
        Rules for differentials
        Differentials of some basic functions
     Higher order derivatives
        Higher derivatives of composite functions examples
        Higher derivatives of implicit functions examples
        Higher derivatives of parametric functions
     Higher order differentials
     L'Hospital's rule - evaluation of limits of indeterminate forms
     Applications of differentiation - the graph of a function and its derivative
     Definition of increasing and decreasing
        Rolle's theorem
        The mean value theorem
        Generalization of the mean value theorem
     Concavity of the graph of a function
        Points of inflection
     Approximate solution to an equation, Newton's method (or Newton-Raphson method)
     Representing polynomial using Maclaurin's and Taylor's formula
        The approximation of the sine function by polynomial using Taylor's or Maclaurin's formula
     Extreme points, local (or relative) maximum and local minimum
        The first derivative test
     Finding and classifying critical (or stationary) points, examples
     Integral calculus - the definite integral
     The area between the graph of a function and the x-axis over a closed interval
        Calculating a definite integral from the definition
     Physical applications of the definite integral
        Describing motion of the objects using velocity - time graphs
     Evaluating the area under the graph of a function using the definition of the definite integral, examples
     The definite and indefinite integrals
     The area between the graph of a function and the x-axis over a closed interval
        Geometric interpretation of the definite integral
     Integration - inverse of differentiation
        Evaluating the indefinite integral
     The fundamental theorem of differential calculus
     The fundamental theorem of integral calculus
        Cavalieri - Gregory formula for quadrature of the parabola
     The indefinite integral
        Basic rules of integration
        Table of indefinite integrals
     Evaluation of indefinite integrals using some basic integration rules and formulas, examples
     Substitution rule
        Evaluating indefinite integrals using substitution rule, examples
     Integration by parts rule
        Evaluating the indefinite integrals using the integration by parts formula, examples
     The indefinite integrals containing quadratic polynomial (trinomial)
        The indefinite integrals containing quadratic polynomial, examples
     Recursion formulas - use of integration by parts formula
     Integrating rational functions
        Use of the partial fraction decomposition to integrate a proper rational function, examples
     The Ostrogradski method of the integration of a proper rational functions
        The Ostrogradski method of the integration of a proper rational functions, examples
     Integrating irrational functions
        Solving irrational functions integrals, examples
        Integrating irrational functions using Euler's substitutions, examples
     Binomial integral
        Solving binomial integrals, examples
     Trigonometric integrals
        Solving trigonometric integrals, examples
        Integrals of rational functions containing sine and cosine
     Integrals of the hyperbolic functions
     Substitution and definite integration
        Substitution and definite integration example
     Integrations by parts and the definite integral
     The improper integrals
     Differentiation and integration of infinite series
        Differentiation of power series
     Applications of the definite integral
     The area of a region in the plane
        The area between the graph of a curve and the coordinate axis
        The area bounded by a parametric curve
        The area in polar coordinates
        The area of the sector of a parametric curve
     The area between two curves
     Length of plane curve, arc length
        Arc length of a parametric curve
        Arc length of a curve in polar coordinates
     The volume of a solid of revolution
        The volume of a sphere
        The volume of a spherical segment
        The volume of a cone
     The surface area of a solid of revolution
        The lateral surface area of a cone
        The surface area of a spherical cap
        The surface area of an ellipsoid
TRIGONOMETRY - solved problems
     Trigonometry
     Degrees to radians and radians to degrees conversion
        Signs of trigonometric functions
     Trigonometric functions of arcs from  0 to 2p
        Trigonometric functions of negative arcs or angles
        Trigonometric functions of complementary angles
        Trigonometric functions of supplementary angles
        Trigonometric functions of arcs that differ on p/2
        Trigonometric functions of arcs that differ on p
     Trigonometric functions of arcs whose sum is 2p
     The values of the trigonometric functions of arcs that are multipliers of 30 (p/6) and 45 (p/4)
        Calculation of values of trigonometric functions of an arbitrary angle x
     Basic relationships between trigonometric functions of the same angle, examples
     Trigonometric identities, examples
     Trigonometric functions and equations
     Trigonometric functions
     Trigonometric equations
     Applications of trigonometry
     Solving right triangles examples
     Solving oblique or scalene triangles examples
     Sections of solids
     Applications of trigonometry in geodesy (or plane surveying) and physics
     An example of using trigonometry in optics
VECTORS - solved problems
     Vectors in a plane
     Addition, subtraction and scalar multiplication of vectors
     Vectors and a coordinate system, Cartesian vectors
        Vectors in a coordinate plane (a two-dimensional system of coordinates), Cartesian vectors, examples
     Vectors in three-dimensional space in terms of Cartesian coordinates
        Vectors in three-dimensional space in terms of Cartesian coordinates, examples
     Scalar product or dot product or inner product
     Vector product or cross product
        An example for the vector product in physics
        The vector product in component form
     The mixed product or scalar triple product expressed in terms of components
     Vector product and mixed product, examples
COORDINATE GEOMETRY - solved problems
     Line in a coordinate plane
     The parametric equations of a line
        The parametric equations of a line examples
     Hessian normal form of the equation of a line
     Distance between a point and a line
     Condition that three points lie on the same line
Points, lines and planes in three-dimensional ( 3D ) coordinate system represented by vectors
     Line in three-dimensional coordinate system
     The parametric equations of a line in 3D
     Equation of a line defined by direction vector and a point - Symmetric equation of a line
        Equation of a line defined by direction vector and a point examples
        The angles that a line forms with coordinate axes
     Angle between lines
     Condition for intersection of two lines in a 3D space
     The equation of a plane in a 3D coordinate system
        The equation of the plane through three points
     The distance of a point and a plane - plane given in general form
     Angle (dihedral angle) between two planes
     Line and plane
        The line of intersection of two planes
        Projection of a line onto coordinate planes
     How determine two planes of which, a given line is their intersection line
        Intersection point of a line and a plane
     Sheaf or pencil of planes
     Points, lines and planes relations in 3D space, examples
        The angle between line and plane
     Point, line and plane - orthogonal projections, distances, perpendicularity of line and plane
        Through a given point pass a line perpendicular to a given plane
        Given a line and a point, through the point lay a plane perpendicular to the line
     Projection of a point onto a plane
     Projection of a point onto a line
        Through a given point lay a line perpendicular to a given line
     Projection of a line onto a plane
        Plane laid through a given point, such that be parallel with two skew lines
        Plane laid through a given point, such that be parallel with two parallel lines
     Distance between point and line
     Distance between point and plane
     Distance between parallel lines
     Distance between two skew lines
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