Determine discontinuities | Jump, gap, and pole (rational functions)

Опубликовано: 29 Август 2026
на канале: MathePeter
47,677
1.1k

A function is continuous if it is not discontinuous. The most important discontinuities are jump points, gaps (removable discontinuities), poles, and essential singularities. In this video, you will learn how to recognize and classify discontinuities and the difference between gaps and poles in rational functions.

Are you interested in weekly support with your exercises and homework in Analysis 1 & Linear Algebra 1? Then feel free to join our study groups!

Math for Engineering:
https://chat.whatsapp.com/EjzxiF8rA67...
https://chat.whatsapp.com/CL3dvXnXe9d...

Math Bachelor's Degree/ Math Teacher Training/ Computer Science, Engineering:
https://chat.whatsapp.com/GANQtu6V78W...

Math in Economics:
https://chat.whatsapp.com/L4iEb7WCaFc...

If you need to prepare for a math exam, check out my own online platform: https://champcademy.com. There you'll find courses, personalized support, and everything you need to pass your exam.

🤓 ONLINE COURSES 🤓
25% discount on all my courses. Coupon code "MATHEPETER"

THEMED COURSES

Statistics and Probability Calculus
https://champcademy.teachable.com/p/s...

Complex Numbers
https://champcademy.teachable.com/p/c...

Sequences, Series, and Difference Equations
https://champcademy.teachable.com/p/s...

Differential Calculus
https://champcademy.teachable.com/p/d...

Limits of Functions
https://champcademy.teachable.com/p/l...

Integral Calculus
https://champcademy.teachable.com/p/i...

Multidimensional Integral Calculus
https://champcademy.teachable.com/p/m...

Functions with Multiple Integers Variables
https://champcademy.teachable.com/p/f...

Extreme Value Calculus
https://champcademy.teachable.com/p/e...

Higher-Order Differential Equations
https://champcademy.teachable.com/p/h...

MODULE COURSES

Mathematics in Economics
https://champcademy.teachable.com/p/m...

Math 1 Crash Course (adapted for HU Berlin)
https://champcademy.teachable.com/p/m...

Math 2 LIVE Crash Course (for HU Berlin)
https://champcademy.teachable.com/p/m...

Statistics 1 LIVE Crash Course (for HU Berlin)
https://champcademy.teachable.com/p/s...

Analysis 1 & Linear Algebra for Engineering (TU Berlin)
https://champcademy.teachable.com/p/a...

Analysis 2 for Engineering (TU Berlin)
https://champcademy.teachable.com/p/a...

BUNDLE

All-In-One Complete Bundle
https://champcademy.teachable.com/p/a...

Topic Course Bundle
https://champcademy.teachable.com/p/a...

SOCIAL MEDIA
https://linktr.ee/mathepeter
  / mathepeter.tv  
  / discord  

CALENDAR
https://kalender.digital/19534f26d000...

AFFILIATE LINKS
I receive a small commission for every purchase. The price remains the same for you:

My calculator
https://amzn.to/2RbhKKj

My blackboard
https://amzn.to/2WdVUtd

♥♥♥ ♜♞♝♛♚♝♞♜ ♥♥♥
♟♟♟♟♟♟♟♟♟
---------------------------------------------------------------------
Would you like to support me?
Patreon:   / mathepeter  
PayPal: https://paypal.me/peterlehe1?locale.x...
--------------------------------------------------------------------
♙♙♙♙♙♙♙♙
♥♥♥ ♖♘♗♕♔♗♘♖ ♥♥♥

Content:
0:00 What to expect
0:22 Jump point
1:29 Gaps & poles in general
1:57 Gaps & poles in rational functions
3:23 Example function 1
4:42 Example function 2
6:13 Essential singularities
6:49 #ADVERTISING