Applying Discontinuity Concepts Quiz

1) A function f is discontinuous at a if:

F(a) does not exist

Lim f(x) does not exist

Lim f(x) != f(a)

F is differentiable at a

Discontinuous if value missing, limit missing, or mismatch.

Explanation

Discontinuous if value missing, limit missing, or mismatch.

Submit

Applying Discontinuity Concepts Quiz - Quiz

How well can you apply discontinuity concepts to real functions? This quiz guides you through analyzing limits, evaluating undefined points, and classifying different types of discontinuities. You’ll work with rational expressions, trigonometric functions, oscillatory functions, and piecewise-defined functions to determine what kind of discontinuity occurs and why. Through these examples,... see moreyou’ll learn how discontinuities arise and when redefining a function can make it continuous. By the end, you’ll be able to identify and explain discontinuities in a wide range of functions with confidence!
see less

2)

What first name or nickname would you like us to use?

You may optionally provide this to label your report, leaderboard, or certificate.

2) Which is a property of removable discontinuity?

Limit exists and is finite

Function value differs or undefined

Function approaches infinity

Left and right limits differ

Removable: limit exists but value wrong/missing.

Explanation

Removable: limit exists but value wrong/missing.

Submit

3) A jump discontinuity occurs when:

Both one-sided limits exist

One-sided limits equal

One-sided limits finite and unequal

F(a) undefined

Jump: finite unequal one-sided limits.

Explanation

Jump: finite unequal one-sided limits.

Submit

4) Infinite discontinuities occur when:

|f(x)| → ∞

Limit is finite

F(a) undefined

One-sided limits diverge

Infinite: vertical asymptote.

Explanation

Infinite: vertical asymptote.

Submit

5) Oscillatory discontinuities occur when:

Function oscillates

Limit fails due to oscillation

F(a)=limit

Sin(1/x) near 0 is example

Oscillation prevents limit.

Explanation

Oscillation prevents limit.

Submit

6) For f(x)=(x^2-1)/(x-1):

Removable discontinuity at 1

Jump discontinuity

Limit = 2

Continuous if f(1)=2

Simplifies to x+1 except at 1.

Explanation

Simplifies to x+1 except at 1.

Submit

7) Consider f(x)=1/|x| at x=0:

Limit exists

Limit infinite

Infinite discontinuity

Jump discontinuity

1/|x|→∞.

Explanation

1/|x|→∞.

Submit

8) For f(x)=tan(x), discontinuities at:

X=2

X=2+k

Only integers

Cos(x)=0

tan undefined when cos=0.

Explanation

tan undefined when cos=0.

9) Which functions are discontinuous at 0?

1/x

|x|

Floor(x)

Sin(1/x)

1/x infinite; floor jump; sin1/x oscillatory.

Explanation

1/x infinite; floor jump; sin1/x oscillatory.

Submit

10) Typical rational hole problem:

Discontinuous at 2

Removable

Jump

Continuous

Standard removable hole.

Explanation

Standard removable hole.

11) If infinitely many jump discontinuities on (0,1):

Discontinuous on dense set

Not Riemann-integrable

Possibly integrable

Vertical asymptote

Dense jumps but integrable if measure zero.

Explanation

Dense jumps but integrable if measure zero.

Submit

12) For f(x)=1/(x-1) at x=1:

Infinite discontinuity

Vertical asymptote

Limit not finite

Jump

1/(x-1)→∞.

Explanation

1/(x-1)→∞.

Submit

13) Discontinuity of 1/(x^2-9) at x=3:

Infinite

Jump

Removable

Vertical asymptote

Denominator zero → asymptote.

Explanation

Denominator zero → asymptote.

Submit

14) For f(x)=|x|/x:

No points

X=0

Jump

Infinite

Sign function jumps.

Explanation

Sign function jumps.

Submit

15) Which are discontinuous on measure-zero set?

Step functions

Floor

Dirichlet

Finite jump functions

Dirichlet is not measure-zero.

Explanation

Dirichlet is not measure-zero.

Submit