Real Analysis | Uniformly Continuity in One Shot by GP Sir

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Real Analysis | Uniformly Continuity in One Shot by GP Sir
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Dr.Gajendra Purohit

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gajendrapurohit-GATE-NET-JAM

In first question: for negative value f(x) is discontinuous as it gives imaginary number ..

Right explanation: f(x) is uniformly continuous on interval (a, b) or [a, b] where 0<a<b< infinity .. f(x) is not only uniformly continuous on closed interval . it can be on open interval.
So option D is not correct.

Correct me if I am wrong 😊

soumodipdas

Product of two u.c is not u.c for example take f(x)=g(x)=x in R, here f and g both are u.c but f.g equal to x^2 which is not u.c in R

faruksk

Sir question number 6 me problem hai thodi, kyoki f(x)=x, agr ye function le to ye UC on R but infinity pr limit nhi exists krti h

manishkumarverma

Sir ek cheez batana Jo aapne first ques karaya, us ques mein derivative wala test aapne use kiya but derivative wale mein end points pe limit kaha hi nikalte hain

_shavyaGarg_MH

Product of Two UC need not UC, example f(x)=x on R

SasiKumar-ilod

Unacadmy pr class li thi same question tha but option D was wrong

abcdWxyz-xmht

F(x) =x where then if use the concept of lipschitz function f(x) ka deriative 1which is bounded then uniformly continius
But in this same question put - infinity and + infinity then fuction does not exist then f not u.c .... aise kaiseho skta h sir

rinkubaswala

Sir super explaination excellent performance

DineshKumar-cyez

Sir dill se izaat karta hn ap ki or hamesha krunga jitna aap se seekha he shayad kisi se nh❤️

tthassi

Sir prod of uc is not uc. Product is uc only if it is bdd, know clarify my doubt sir

sathyam

What about f(x) = sinx on [0, infinity)

mudasirbashir

So plese sir help me to solve this question

rinkubaswala

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