Continous Function Part:1 | Function Of Several Variables | IIT JAM | CUET PG 2027 | Lec-3 | IFAS

(Continous Function Part:1 | Function Of Several Variables | IIT JAM | CUET PG 2027 | Lec-3 | IFAS) explained with clear concepts and exam-focused approach. Master Continuous Function Part‑1 for IIT JAM & CUET PG 2027 with PYQs, continuity tricks, and problem‑solving.

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⏳ Lecture Timeline:
[00:00:00] – Introduction of Continous Function Part:1
[00:05:03] – Definition: Continuity in R²
[00:06:30] – Formal Definition with ε‑δ
[00:09:00] – Note: Isolated Points & Automatic Continuity
[00:11:23] – Question 1: Check Continuity f=xy/(x²+y²)
[00:13:58] – Trick: Polar Form for Limit
[00:15:42] – Key Points: Continuity on Domain
[00:18:34] – Note: Partial Continuity ≠ Total Continuity
[00:18:57] – Example: Slices Continuous but Function Not
[00:22:51] – Question 2: f=x²/(x²+y²) – Continuity, Limits, Bounded
[00:28:39] – Question 3: f=xy/(x²+y²) – Continuity, Boundedness, Integral
[00:35:40] – Question 4: Find k for Continuity at Origin
[00:40:23] – Question 5: Domain Excluding y‑axis, f=x sin(1/y)
[00:47:10] – Question 6: f=x²y/(x²+y²) – Continuity, Repeated Limits, Bounded
[00:51:01] – Question 7: f=x sin(1/y) + y sin(1/x) – Limit, Repeated Limits
[00:54:45] – Complete Session (Continuity of Several Variables)


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📖 Topics Covered in This Lecture:
• Continuity in R² (ε‑δ Definition)
• Limit‑Based Continuity Check
• Isolated Points & Discrete Sets
• Counterexamples: Repeated Limits
• Boundedness & Limit Existence
• PYQ Practice & Quick Tricks


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📚 Lecture Summary:
In this session, IFAS Expert Faculty focuses on Continuous Function Part‑1, covering the ε‑δ definition for functions of several variables, continuity via limits, and isolated points. Learn to check continuity using polar forms, repeated limits, and boundedness. Solve IIT JAM & CUET PG 2027 PYQs with smart tricks. Strengthen your Continuous Function and limit concepts with this Lec‑3.


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🎓 This lecture is highly beneficial for students preparing for:
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✅ CUET PG Mathematics
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✅ NBHM Mathematics

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