## 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

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 or search me on Google * Share among your peers as SHARING is CARING!!

CONTINUITY 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) 1-cos 4x Ex. If f(x) = x2 is continuous then the value of a- x=0 (2) 1 (3) 4 Sol(4) Since the given function is continuous at x = 0 2sin2 2x 4 4 lim 1-cos4x 2 2 sin 2x MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) X-11 1-x +a, x>1 Iff(x) = (a+b, x=1 is continuous at x = 1 ten the value of a & b are respectively Ex.6 +b, x<1 1-X (3) 2, 3 (4) None of these Sol.(2) f1)- ab f(1 + h) = . 1-11+h) :given function is continuous |1-h-1h -h-1-(1-hi Now MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) log(1 +2ax) log(1-bx) Ex. If f(x)- If function is continuous at x0 then the value of k (2) 2a b (3) a (4) 0 1+2ax 1-bx 1-bx) (2a) -(1 +2ax)(-b) Sol.(2) im Applying L' hospital rulel (1- bx) x-0 (2a+b) - 2a+ b (1)(1) 2a+ b lim x 0 (1-bx)(1+2ax) MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) (1) Discuss the continuity of f (x)e +1 at the point x 0 0 h 0 l/h h 0 Divide N and D by elh to get: 1/h L. H.L. R.H.L.-,f(x) is discontinuous at x = 0 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Function fix)-X*-1 is discontinuous at- 2 x -3x +2 (2) x = 1, 2 (3) x = 2 (4) No where Sol. (2) Every function is discontinuous at the points which are not in its domain (x2 -1) f(x)#, (x-1)(x-2) so function is discontinuous at x = 1, 2 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) cosx-sin x The function f(x) - is continuous everywhere then f( /4) cos 2x (2) 1 (4) 1/ 01. (4) Function is continuous every where then it will continuous at x =- 4 0 = lim cosx-sinx form 0 4 By L'hospital rule = lim -sin x-cosx_ -sin / 4-cos / 4 2 4 x / 2 2 sin 2x 4 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!!