## Vineet Loomba is teaching live on Unacademy Plus

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

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!!

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)

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)

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)

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)

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)

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!!