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Examples on Continuity of a Function at a point
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In this lesson examples on continuity have been discussed

Vineet Loomba is teaching live on Unacademy Plus

Vineet Loomba
IITian | No. 1 Educator in IIT-JEE (Maths) | 4 Million Minutes Watch Time | 8+ Years Experience | Youtube: Maths Wallah | vineetloomba.com

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Present chief election commissioner - Om Prakash Rawat and other two - Sunil Arora and Ashok lavasa
Hari Singh Rajput
9 months ago
Good
AM
hi sir, in example 2, u applied u/v rule for log vala term then, why didn't u applied it for log vala term/x
x^2-1/ x^2 -3x +2 is discontinuous at x=2 nahi hona chaiye tha sir kyuki factorise karne ke baad (x+1)(x-1)/(x-1)(x-2) aa jayega or (x-1) num or denominator se cancel ho jayega toh denom me (x-2) hi bachega end me?
Vineet Loomba
3 months ago
Function is not defined at x=2 ..it will definitely be discontinuous there
last example after applying l hospital rule how dominator becomes once again multiplied by 2 it is a silly doubt sorry to trouble
Vineet Loomba
3 months ago
that is by chain rule of differentiation
and sir,uv rule in the denominator v should be differentiated.
Vineet Loomba
3 months ago
which question? timestamp
y should we reciprocate @5.03
Vineet Loomba
3 months ago
because log x diff is 1/x .. so if u will do it on paper u will find it be reciprocating ..
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  4. 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)


  5. 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)


  6. 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)


  7. 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)


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  9. 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)


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