Mathematics 108, Introduction to Differential Calculus ... |
From inside the book
Results 1-3 of 9
Page 9
... ( x ) be a function , the range of the independent variable being some set of ... f ( x ) be a function , the range of x being R ; we say f ( x ) is defined in the neighborhood of a if any interval ... interval containing a must contain an ...
... ( x ) be a function , the range of the independent variable being some set of ... f ( x ) be a function , the range of x being R ; we say f ( x ) is defined in the neighborhood of a if any interval ... interval containing a must contain an ...
Page 10
... interval 2.05 < x < 2.3 . Hence f ( x ) > 2.5 in the neighborhood of 2.1 . Is this true in the neighborhood of 2 ? The answer is no for an interval containing 2 contains numbers 2 and at these points the value of the function is < 2 and ...
... interval 2.05 < x < 2.3 . Hence f ( x ) > 2.5 in the neighborhood of 2.1 . Is this true in the neighborhood of 2 ? The answer is no for an interval containing 2 contains numbers 2 and at these points the value of the function is < 2 and ...
Page 16
... interval ( a , b ) and does not vanish at any point of this interval then is also continuous on this interval . 9 . 10 . If f ( x ) is continuous on ( a , b ) and its end points , f ( x ) is bounded on ... f ( x ) a discontinuous f ( x ) 16.
... interval ( a , b ) and does not vanish at any point of this interval then is also continuous on this interval . 9 . 10 . If f ( x ) is continuous on ( a , b ) and its end points , f ( x ) is bounded on ... f ( x ) a discontinuous f ( x ) 16.
Common terms and phrases
absolute value bers bounded function bounded set bounds we say consider contain other points contain points containing a contains continuous functions continuous on a,b Corollary define a function defined for integral denote dependent discontinuous dy dx end points endless number Example Exercises exists an interval finite number frontier number function f(x function is bounded function is defined greatest lower bound greatest number h₁(x h₂(x Hence f(x incommensurable increment integers integral values interval a,b interval containing interval f(x irrational numbers least upper bound Lemma Let f(x Lima limit as x Limx means of deciding negative non-negative pair of points polynomial positive number problem Proof Properties of Continuous range rational numbers say f(x say the set second characteristic set is bounded set is infinite set of numbers set of points statement terval Theorem 6.2 Theorem 9.2 true values of f(x ха