Engineering Mathematics 06 | Continuity and Differentiability | GATE - For All Branches

The lecture begins with a clear definition of Continuity, explaining the three essential conditions a function must satisfy at a point, including the concept of left-hand and right-hand limits. Following this, the session dives into Differentiability, establishing the necessary conditions for a function to be differentiable and exploring the relationship between continuity and differentiability—a common area for conceptual questions in GATE. We will cover standard differentiation rules, the chain rule, and solve challenging GATE previous year questions (PYQs) and examples involving piecewise functions and absolute value functions to ensure you master these concepts for your exam preparation. 📕 𝐁𝐚𝐭𝐜𝐡/𝐂𝐨𝐮𝐫𝐬𝐞 𝐋𝐢𝐧𝐤𝐬:- GATE GURUKUL Course Link - https://www.geeksforgeeks.org/courses/gate-premium All courses - https://www.geeksforgeeks.org/courses/category/gate?utm_source=youtube&utm_medium=livestreams&utm_campaign=gatelivesessions GATE Agni Pariksha Batch Link - https://www.geeksforgeeks.org/payments/gate-cse-agni-pariksha GATE 2026 CS & IT Test Series Link - https://www.geeksforgeeks.org/courses/gate-cse-it-test-series-2026 GATE 2026 DA Test Series Link - https://www.geeksforgeeks.org/courses/gate-da-testseries-2026 Mission ISRO CSE - https://www.geeksforgeeks.org/courses/mission-isro-cse Mission ISRO ECE - https://www.geeksforgeeks.org/courses/mission-isro-ece GATE SPL. Combo Course - CSIT + DA 2026 (Combo course) - https://www.geeksforgeeks.org/courses/gate-csit-da-2026?utm_source=youtube&utm_medium=livestreams&utm_campaign=gatelivesessions (With Placement Prep) - https://www.geeksforgeeks.org/courses/gate-2026-placement-csit-da?utm_source=youtube&utm_medium=livestreams&utm_campaign=gatelivesessions GATE CSE Weekday (2026) - https://www.geeksforgeeks.org/courses/gate-2026-csit?utm_source=youtube&utm_medium=livestreams&utm_campaign=gatelivesessions (2027) - https://www.geeksforgeeks.org/courses/gate-2027-csit?utm_source=youtube&utm_medium=livestreams&utm_campaign=gatelivesessions (2028) - https://www.geeksforgeeks.org/courses/gate-2028-csit?utm_source=youtube&utm_medium=livestreams&utm_campaign=gatelivesessions GATE CSE Weekend (2026) - https://www.geeksforgeeks.org/courses/gate-2026-csit-weekend?utm_source=youtube&utm_medium=livestreams&utm_campaign=gatelivesessions GATE CSIT With Placement Preparation Complete Course (2026) - https://www.geeksforgeeks.org/courses/gate-2026-placement-csit?utm_source=youtube&utm_medium=livestreams&utm_campaign=gatelivesessions GATE Rank Booster With Expert - Curated Questions - https://practice.geeksforgeeks.org/courses/gate-rank-booster GATE CSIT With Placement Preparation Complete Course (2027) - https://www.geeksforgeeks.org/courses/gate-2027-placement-csit?utm_source=youtube&utm_medium=livestreams&utm_campaign=gatelivesessions (2028) - https://www.geeksforgeeks.org/courses/gate-2028-placement-csit?utm_source=youtube&utm_medium=livestreams&utm_campaign=gatelivesessions GATE SPL. Combo Course - CSIT + DA (2027) - https://www.geeksforgeeks.org/courses/gate-csit-da-2027?utm_source=youtube&utm_medium=livestreams&utm_campaign=gatelivesessions (2027 + Placement Prep.) - https://www.geeksforgeeks.org/courses/gate-2027-placement-csit-da?utm_source=youtube&utm_medium=livestreams&utm_campaign=gatelivesessions (2028) - https://www.geeksforgeeks.org/courses/gate-csit-da-2028?utm_source=youtube&utm_medium=livestreams&utm_campaign=gatelivesessions (2028 + Placement Prep.) - https://www.geeksforgeeks.org/courses/gate-2028-placement-csit-da?utm_source=youtube&utm_medium=livestreams&utm_campaign=gatelivesessions Gate CSE Semester & Placement Preparation (2027) - https://www.geeksforgeeks.org/courses/gate-cse-2027-semester-placement?utm_source=youtube&utm_medium=livestreams&utm_campaign=gatelivesessions (2028) - https://www.geeksforgeeks.org/courses/gate-cse-2028-semester-placement?utm_source=youtube&utm_medium=livestreams&utm_campaign=gatelivesessions For any query visit https://www.geeksforgeeks.org/courses/category/gate Or reach us at +91-08069289001 RECOMMENDED CHANNELS FOR YOU: GeeksforGeeks GATE EE/EC/IN - https://www.youtube.com/@GfG_EC_EE_IN GeeksForGeeks GATE English - https://www.youtube.com/@GeeksforGeeksGATEEnglish 📚 Stay tuned for more Maha Marathon sessions on all GATE topics! 💬 Don't forget to comment your doubts and feedback! 👉 Subscribe to our channel for more GATE preparation content and hit the 🔔 to never miss an update! 👍 Like | 🔄 Share | 📢 Spread the word #Continuity #Differentiability #Calculus #EngineeringMathematics #GATE2026 #GATEPreparation #MathsForGATE #GATEForAllBranches #DifferentiationRules #PiecewiseFunctions #GATEForEngineeringMathematics #EngineeringMathematicsForGATE #EngineeringMathematicsBySakshiMam #GfG #GfGGATE