This is a practical way to define continuity. An easy way to test it is by examining whether the pen can trace the function graph without being lifted from the paper. The inverse of a trigonometric function f may be indicated using the inverse function notation f - 1 or with the prefix "arc" (e.g.The basic concept of continuity is a crucial part of calculus.In this test, l n x denotes the natural logarithm of x (that is, the logarithm to the base e).The range of f is assumed to be the set of all real numbers f ( x ) where x is in the domain of f. Unless otherwise specified, the domain of any function f is assumed to be the set of all real numbers x for which f ( x ) is a real number.Unless otherwise specified, all angles are measured in radians, and all numbers used are real numbers.Straight lines and smooth curves may appear slightly jagged. The figures are drawn as accurately as possible except when it is stated in a specific question that the figure is not drawn to scale. All figures lie in a plane unless otherwise indicated. Figures that accompany questions are intended to provide information useful in answering the questions.Other (e.g., accumulated change from a rate of change).Average value of a function on an interval.The Fundamental Theorem: d d x ∫ a x f ( t ) d t = f ( x ) and ∫ a b F ' ( x ) d x = F ( b ) - F ( a ).Definition of the definite integral as the limit of a sequence of Riemann sums and approximations of the definite integral using areas of rectangles.Solutions of y ' = k y and applications to growth and decay.Distance and velocity from acceleration with initial conditions.Integration by substitution (use of identities and change of variable). Integral Calculus (40%) Antiderivatives and Techniques of Integration
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