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In this problem-solving session Chandan Sir from IFAS provides an intensive look at Finite Dimensional Vector Spaces and Real Analysis. This lecture is specifically designed for IIT JAM Mathematics and CUET PG aspirants, focusing on applying theoretical concepts to competitive exam questions as the exam date approaches. 🔥 Join India's Best Mathematics Coaching for IIT JAM and CUET PG Exams - IFAS Online! STARTING SOON: Champion 2.2 Batch (From 19 Feb 2026) 👉🏻 IFAS IIT JAM and CUET PG Mathematics Result👈🏻: 🌟 IIT JAM 2025 - Total Selections: 1000+ (IIT JAM AIR 1,3,4,6,7,8....) 🌟CUET PG 2025 - Total Selections: 1500+ 🌟IIT JAM 2024: Total Selections: 800+ (IIT JAM AIR 1, 2, 3, 4, 8, 10...) 🌟CUET PG 2024: Total Selections: 500+ 🌟IIT JAM 2023: Total Selections: 600+ (IIT JAM AIR 1, 2, 8, 9...) 🌟IIT JAM 2022: Total Selections: 500+ (IIT JAM AIR 1, 4, 7, 10...) ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 👇 Watch the Full Lecture to Master These Topics: Properties of Continuous Functions Dirichlet-type Functions Topology of Discontinuity Sets Sequence Convergence vs. Boundedness Limits of Sequences & Ratio Test Logarithmic Series & Expansions ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ ⏱️ Timestamps - Jump to Your Topic: [00:01] Introduction [01:28] Problem 1: Continuous Maps and Monotonicity Conditions [06:50] Problem 2: Dirichlet Function Roots and Discontinuity Sets [12:54] Problem 3: Continuity of Integral-defined Functions using Leibniz Rule [16:40] Problem 4: Limit Evaluation of Sequences via Ratio Test [22:42] Problem 5: Combining Convergent and Bounded Sequences [27:22] Problem 6: MSQ on Logarithmic Sequence Limits and Series Expansions [34:10] Problem 7: Set of Continuous Points and Path-connectedness [40:40] Problem 8: Solving Differential Inequalities for Function Values ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ Lecture Summary: In this session, Chandan Sir emphasizes the application of theory over rote memorization, specifically for students with only days remaining before the IIT JAM exam. The lecture covers a broad spectrum of Real Analysis, from the fundamentals of one-variable functions to the complexities of multivariable continuity and sequence convergence. Chandan Sir uses interactive polls to engage students and provides counter-examples to debunk common misconceptions about bounded and oscillating sequences. He concludes by encouraging students to attempt the 18 free mock tests available on the IFAS platform to solidify their preparation. ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 🔗 Important Links: 🌍 Visit our Website: https://ifasonline.com/iit-jam/mathem... 📞 Contact for Queries: 9172266888 📲 WhatsApp: https://whatsapp.com/channel/0029VbCV... 📘 Get Detailed Free Counselling: https://ifasonline.com/iit-jam/mathem... ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ Download IFAS: 👇 📲Android: https://play.google.com/store/apps/de... 📲 Ios: https://apps.apple.com/us/app/ifas/id... ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ IIT JAM Mathematics Live & Recorded Course – https://ifasonline.com/iit-jam/mathem... CUET PG Mathematics Live & Recorded Course – https://ifasonline.com/cuet-pg/mathem... Buy IIT JAM Mathematics Books – https://ifasonline.com/cuet-pg/mathem... ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 📞 Contact for Admission: 9172266888 Stay Updated Via Other Social Media: ✔Telegram Discussion Group: https://t.me/IITJAM_NBHM_MScEntranceM... ✔Instagram: / ifas_maths__iit_jam_cuet_nbhm ✔Facebook: / mscentrancemaths ✔WhatsApp: https://api.whatsapp.com/send?phone=9... ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ #iitjam #iitjammathematics #iitjammaths #iitjammath #mathematics #cuetpgmathematics #cuetpg #ifas #tifr