O'Reilly logo

FUNDAMENTALS OF MATHEMATICS DIFFERENTIAL CALCULUS by Sanjay Mishra

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

TEXTUAL EXERCISE–1: (OBJECTIVE)
  1. (d) ∵ discontinuity exists due to

    (i) Non-existence of limit i.e., Either L.H.L ≠ R.H.L or any one of these are infinite or does not exist uniquely.

    (ii) images and all polynomials are continuous function whatever may be its degree.

  2. (a) f (0- ) = f (0+ ) = f (0) = a

    images

    a = 0

  3. (d) f (x) = [x]2 - [x2 ] and let k ∈ ℤ, then

    images

    ∴ For continuity at k;

    ⟹ (k - 1)2 < (k + h)2 < (k - 1)2 + 1 and k2 < (k + h)2 < k2 + 1 for h → 0+

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required