Continuity of Functions and Discontinuity Types

Описание: 📗 Welcome to BOSSDOMX Learning Hub, your complete Class 12 Maths guide!

In this video, we explore the concept of Continuity of Functions — one of the most important and conceptual topics in calculus.
You’ll learn how to check continuity at a point, over an interval, and understand the types of discontinuities with crystal-clear visual examples and solved problems.

Perfect for Class 12 Boards, JEE, and NEET aspirants, this lesson makes every concept easy to grasp.

📘 Topics Covered:

✔️ Definition of a Continuous Function
✔️ Continuity at a Point and in an Interval
✔️ Left-hand Limit (LHL) & Right-hand Limit (RHL)
✔️ Condition for Continuity
✔️ Types of Discontinuity
 🔹 Removable Discontinuity
 🔹 Jump Discontinuity
 🔹 Infinite Discontinuity
 🔹 Oscillatory Discontinuity
✔️ Graphical Interpretation of Continuity
✔️ Step-by-Step Solved Examples

💡 Learning Outcomes:

After this video, you’ll be able to:
🔹 Define and check continuity using limits.
🔹 Identify points of discontinuity in any function.
🔹 Classify discontinuities into types (removable, jump, infinite, etc.).
🔹 Apply limit and function value conditions correctly.
🔹 Prepare effectively for CBSE Board and JEE Main exams.

🧠 Key Concepts:

For a function
𝑓
(
𝑥
)
f(x) to be continuous at x = a,

lim
⁡
𝑥
→
𝑎
−
𝑓
(
𝑥
)
=
lim
⁡
𝑥
→
𝑎
+
𝑓
(
𝑥
)
=
𝑓
(
𝑎
)
x→a
−
lim
​

f(x)=
x→a
+
lim
​

f(x)=f(a)

If any of these conditions fail → the function is discontinuous.

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📢 Call to Action:

👍 Like this video if the concept of continuity became clear!
💬 Comment any function you want to check for continuity.
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