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Left Hand Limit and Right Hand Limit
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This lesson explains the concept of right hand limit and left hand limit. Also existence of limit has been explained in detail. In the last, important concept of piece wise defined function has been explained with an example.

Vineet Loomba is teaching live on Unacademy Plus

Vineet Loomba
IITian | Best Online Maths Educator | Highest Overall Watch Time | 8+ Years Experience | Youtube: Maths Wallah | vineetloomba.com
U
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Megha Khandelwal
9 months ago
Welcome. Keep learning
Dk
Sir b.tech ka math
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Dk
Sir b.tech ka math
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NG
Nice explanation sir sir mera main ka exam ha january me kya syllabus ha mera please tell me sir
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DM
please make video tutorials for NIMCET examination
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  1. IIT-JEE VIDEO COURSE FOR SURE SHOT SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) IIT-JEE MATHS MADE EASY PREPARED BY: ER. VINEET LOOMBA IITian | IIT-JEE MENtOR Search vineet loomba unacademy" on GOOGLE


  2. REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) ABOUT ME B.Tech. From IIT Roorkee IIT-JEE Mentor Since 2010 Doubts/Feedback in Comment Section * Comment other topics you want to revise. Follow me @ https://unacademy.com/user/vineetloomba to get updates or search me on Google * Share among your peers as SHARING is CARING!!


  3. LIMITS #LHL | RHL | EXISTENCE IIT-IEE MATHS MADE EASY PREPARED BY: ER. VINEET LOOMBA IITiAN | IIT-JEE MENTOR FoR SURE SHoT SUcCESS IN JEE MAIN AND ADVANCED (IIT-JEE)


  4. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Right Hand Limit If f (a) approaches , as x approaches a from right, then , is called as the right hand limit of f (x). Right hand limit can be expressed as m x a Right hand limit can also be expressed as himo (a + h) [Put x=a+h n the above result] h 0 Here h is infinitely small positive number approaching to 0 Left Hand Limit If f (x) approaches 2 as x approaches a from left, then /2 is as called as the left hand limit off(x) Left hand limit can be expressed as:lim /(x-/2 Left hand limit can also be expressed as lim. a-h) [Put x = a-h in the above result] Here h is infinitely small positive number approaching to 0 . MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)


  5. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Existence of Limit ie. For existence of limit at x = a 11 = 12 ,f(x)= lim xa f(x lim MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)


  6. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Important Points to Note: Ifx increases endlessly or can be made larger than any number, then we say that x approaches infinity. In mathematical notation, we write x -o. Infinity (o) is not a fixed number on the number line. Hence no variable can be equal to infinity (o. A variable or an expression can approach o Ordinary laws of algebra cannot be applied to oo. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)


  7. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example#1 Show that the limit of: /x)-2x-1;*51 at x - 1 exists.(JEE Mair) at x = 1 exists. Left hand limit: Right hand limit = rlim-f(x)=hlim0/(l-h) lim f(x)- lim f(1+h) lim 2(1-h)-1 lim 1-2h -1 h-0 Hence limit exists and is equal to 1 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)


  8. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ABOUT ME B.Tech. From IIT Roorkee IIT-JEE Mentor Since 2010 Doubts/Feedback in Comment Section * Comment other topics you want to revise. Follow me @ https://unacademy.com/user/vineetloomba to get updates. * Share among your peers as SHARING is CARING!!