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Mr. Sumit Kumar, was an Integrated PhD student at IISc Bangalore. After that he went to IMSc Chennai to do research in Number Theory. He was also selected at HRI, Allahabad as a PhD student. He secured AIR 01 in JNU-MCA, AIR 05 DU-MCA and AIR 08 PUNE-MCA.

Through his sincerity, dedication and hard work, he earned respect from his students and became very popular amongst the student fraternity, as Sumit Sir, for his in-depth subject knowledge, unmatched teaching skills.

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No word's sir. Amazing video. You always approach the problem using concepts and not just random shortcuts

rishabhkumarsingh

I respect your dedication sir. Thank you so much for your video

ashishjain

When a>0, on [a, 10] , this is uniformly convergent. Actually in this case Mn=1÷(1+n^2 .a^2)

arghamazumder

But the exercise you have have given I am not able to do please help me Sir.

ashishjain

On [a, infinte], a>0 is (fn ) is uniformly cgt.
Reason: fn (x)=1/(1+n^2.x^2) is decreasing function on [a, infinite] and f (x)= lim (fn (x))=0 on [a, infinite] then sup|fn (x)-f (x)|=1/(1+n^2.a^2) which approaches o as n approaches infinte
H.P
Is it right sir??

sajanphutela

Option 4 is not correct since LHS is lim of tan inverse n as n goes to infinity is π/2 not equal to RHS (0)

niharikaawesome

Sir In option 4 how can we take limit function as zero function? Firstly we have seen that limit function is a discontinuous function??? it takes values both 0 and 1 as well...so how to put lim fn(x)= 0 in option 4

chiranjibchoudhury

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