CLASSIFYING TYPES OF DISCONTINIUITY PRACTICE PROBLEMS

Discuss the continuity. If a discontinuity exists, then describe the type of discontinuity and its physical feature on a graph.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Problem 6 :

Solution

For each function identify the type of discontinuity and where it is located.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

f(x) = x³ - 4x

Solution

Problem 4 :

Solution

Problem 5 :

f(x) = sec 2x for 0 ≤ x ≤ 2π

Solution

Problem 6 :

Solution

Problem 7 :

Solution

Problem 8 :

Solution

Problem 9 :

Solution

Problem 10 :

f(x) = csc (x/2) for 0 ≤ x ≤ 2π

Solution

Problem 11 :

The graph of the function 𝑓(𝑥) is shown to the right: Which of the following statements is true about 𝑓?

I. 𝑓 is undefined at 𝑥 = 1.

II. 𝑓 is defined but not continuous at 𝑥 = 2.

III. 𝑓 is defined and continuous at 𝑥 = 3.

(A) Only I     (B) Only II     (C) I and II

(D) I and III      (E) None of the statements are true.

Solution

Problem 12 :

The function f(x) has removable discontinuity at

(A) x = -2 only     (B) x = 0 only    (C) x = 1 only

(D) x = -2 and x = 0 only 

(E) f(x) has no removable discontinuities

Solution

Problem 13 :

On what intervals is f(x) continuous ?

a) [-3, -2] U [-2, 0] U [0, 2.5]      b) [-3, -2] U (-2, 0] U [0, 2.5]

c) [-3, -2] U (-2, 0] U (0, 2.5]  d) [-3, -2] U [-2, 0] U (0, 2.5]

Solution

Problem 14 :

The function has jump discontinuity is at ?

Solution