Real Analysis | Uniformly Continuity in One Shot by GP Sir

[@gajendrapurohit-GATE-NET-JAM]

Thank You for Watching the Video !
Get CSIR NET, IIT JAM, GATE, RPSC Courses, Test Series, Video Lectures, etc on our Mathscare App -
👉 Android - play.google.com/store/apps/details?id=com.mathscare.app
👉 IOS - apps.apple.com/in/app/mathscare/id6467857729
🔹 Telegram Channel - telegram.me/mathsbygpsir
🔹WhatsApp Channel - whatsapp.com/channel/0029Va52c3u5q08jHbUGLO3q

[@soumodipdas7088]

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

[@Mathmystery2.0]

[a,b] pe kyun nahi hoga a toh > 0 hai??? Plz explain

[@jangid9066]

Right because option b has perfect interval than to option d

[@faruksk399]

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

[@faruksk399]

@@harshparmar1942 use the definition of uniform continuty

[@harshparmar1942]

@@faruksk399 Sorry ... My reply was sent unknowingly.

[@faruksk399]

@@harshparmar1942 ok

[@sreya2004]

X is not continous on real numbers, it is only continous when it is bounded between two given values

[@shilpavk-n7l]

36:46 here in question they have given x>0 ,

[@diwakarmishra108]

Good explanation every line.

[@SanjuDevi-u8l2e]

Very helpful video thank u sooooo.... Much sir

[@t4thassi750]

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

[@rinkubaswala6973]

F(x) =x where f:R........R 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

[@manishkumarverma3486]

Wahi to mai bhi keh rha hoon ji

[@atishff5531]

Any 1 condition should be satisfied

[@SasiKumar-il8od]

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

[@Bharat_865]

Thanks sir ji 🙏

[@DineshKumar-cy3ez]

Sir super explaination excellent performance

[@abcdWxyz-xm5ht]

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

[@manishkumarverma3486]

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

[@hariomgupta9116]

Manish ji if function does not exist -inf. and inf. Then we can not say function is uniform continuous or not but if function is exist both -inf. and inf. then function is uniform continuous.

[@manishkumarverma3486]

@@hariomgupta9116 but jara LF ki condition lga k dekho, function LF hai mtlb Lipschitz function hai ye aur LF impliesUC

[@hariomgupta9116]

@@manishkumarverma3486 logic to aap sahi lga rahe hain but jo LF hota hai wo subset of real no. me define hota hai, ya kisi finite interval me define hota hai but aap jis example ki baat kar rahe Hain wo R me define hai

[@happinessforever4187]

You are right 👍

[@hariomgupta9116]

@@happinessforever4187 thanks 👍

[@_shavyaGarg_MH]

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

[@montymonty3145]

Thank you sir 🙏🙏🙏🙏🙏🙏

[@ruchithakur4381]

Thank you sir😊

[@ankitarajputankitarajput116]

Thnkuuuuuuuuu guru ji🎉🎉🎉

[@mudasirbashir1795]

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

[@ruchichawla9940]

Thanku so much sir

[@sathyam909]

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

[@indukant2493]

Maja aa gaya sir

[@sheewaligarg]

Thanku sir ❤

[@rajputzadii-b4e]

sir q2 ky solution ki pdf share kr dy

[@trilokinath6633]

B option

[@rinkubaswala6973]

So plese sir help me to solve this question

[@manishkumarverma3486]

To I think option B is true

[@shrawankumarpatel2148]

🙏🌺🌺🌺🙏