Quiz (Continuity of a Function)

(1) Find constants and so that the functions will be continuous for all in the domain.

    (a)

    (b)
    
    (c)

(2) Let and . Show that



(3) If a function is not continuous at , but can be made continuous at by being assigned a new value of that point, it is said to have a removable discontinuity at Which of the following functions have a removable discontinuity at ?

    (a) at
    
    (b) at
    
    (c) at
    
(4) Prove that the following functions have at least one real root.

    (a)
    
    (b)

(5) Find a function(s) with the following properties.

    (a) Find functions and such that is discontinuous at but is continuous there.

    (b) Give an example of a function defined for all real numbers that is continuous at only one point.

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Cite this as:
Continuity Quiz
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/continuity-quiz.html