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NCERT Class 12 Maths Chapter 5: Continuity And Differentiability 34 Questions Solved

NCERT Solutions for Class 12 Maths Chapter 5 Continuity And Differentiability — Exercise 5.1

Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.

Prove f(x)=5x−3 is continuous at x=0,−3,5.

Examine continuity of f(x)=2x²−1 at x=3.

Examine continuity: (a) x−5; (b) 1/(x−5), x≠5; (c) (x²−25)/(x+5), x≠−5; (d) |x−5|.

Prove f(x)=xⁿ is continuous at x=n, for a positive integer n.

Is f(x)=x for x≤1 and f(x)=5 for x>1 continuous at 0,1,2?

Discuss continuity and find any discontinuities of f(x)=2x+3 for x≤2; 2x−3 for x>2.

Discuss continuity and find any discontinuities of f(x)=|x|+3 for x≤−3; −2x for −3<x<3; 6x+2 for x≥3.

Discuss continuity and find any discontinuities of f(x)=|x|/x for x≠0; 0 for x=0.

Discuss continuity and find any discontinuities of f(x)=x/|x| for x<0; −1 for x≥0.

Discuss continuity and find any discontinuities of f(x)=x+1 for x≥1; x²+1 for x<1.

Discuss continuity and find any discontinuities of f(x)=x³−3 for x≤2; x²+1 for x>2.

Discuss continuity and find any discontinuities of f(x)=x¹⁰−1 for x≤1; x² for x>1.

Discuss continuity and find any discontinuities of f(x)=x+5 for x≤1; x−5 for x>1.

Discuss continuity and find any discontinuities of f(x)=3 for 0≤x≤1; 4 for 1<x<3; 5 for 3≤x≤10.

Discuss continuity and find any discontinuities of f(x)=2x for x 1.

Discuss continuity and find any discontinuities of f(x)=−2 for x≤−1; 2x for −1 1.

Find the relation between a,b for f(x)=ax+1 (x≤3), bx+3 (x>3) to be continuous at 3.

Can f(x)=λ(x²−2x) for x≤0 and 4x+1 for x>0 be continuous at 0? What about 1?

Show that g(x)=x−⌊x⌋ is discontinuous at every integer.

Is f(x)=x²−sin x+5 continuous at π?

Discuss continuity of (a) sin x+cos x, (b) sin x−cos x, (c) sin x cos x.

Discuss continuity of cosine, cosecant, secant and cotangent.

Find all discontinuities of f(x)=sin x/x for x<0 and x+1 for x≥0.

Is f(x)=x² sin(1/x) for x≠0, f(0)=0 continuous?

Examine continuity of f(x)=sin x−cos x for x≠0, f(0)=−1.

Find k for f(x)=k cos x/(π−2x) for x≠π/2 and 3 at π/2, continuous at π/2.

Find k for f(x)=kx² for x≤2 and 3 for x>2, continuous at 2.

Find k for f(x)=kx+1 for x≤π and cos x for x>π, continuous at π.

Find k for f(x)=kx+1 for x≤5 and 3x−5 for x>5, continuous at 5.

Find a,b so f(x)=5 for x≤2, ax+b for 2<x<10, and 21 for x≥10 is continuous.

Show cos(x²) is continuous.

Show |cos x| is continuous.

Show sin|x| is continuous.

Find discontinuities of f(x)=|x|−|x+1|.