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JEE Main 2019 · 9 April · Shift II

JEE Main 2019 Mathematics question on Limits Continuity and Differentiability

If f(x)=[x]−[x4]f(x) = [x] - \left[\frac{x}{4}\right], x∈Rx \in R where [x][x] denotes the greatest integer function, then
(a) lim⁡x→4+f(x)\lim_{x \to 4+} f(x) exists but lim⁡x→4−f(x)\lim_{x \to 4-} f(x) does not exist
(b) ff is continuous at x=4x = 4
(c) Both lim⁡x→4−f(x)\lim_{x \to 4-} f(x) and lim⁡x→4+f(x)\lim_{x \to 4+} f(x) exist but are not equal
(d) lim⁡x→4−f(x)\lim_{x \to 4-} f(x) exists but lim⁡x→4+f(x)\lim_{x \to 4+} f(x) does not exist
  1. A.
    lim⁡x→4+f(x)\lim_{x \to 4+} f(x) exists but lim⁡x→4−f(x)\lim_{x \to 4-} f(x) does not exist
  2. B.
    ff is continuous at x=4x = 4
  3. C.
    Both lim⁡x→4−f(x)\lim_{x \to 4-} f(x) and lim⁡x→4+f(x)\lim_{x \to 4+} f(x) exist but are not equal
  4. D.
    lim⁡x→4−f(x)\lim_{x \to 4-} f(x) exists but lim⁡x→4+f(x)\lim_{x \to 4+} f(x) does not exist
Show answer

Correct option: B

[JEE Main 2019 · 9 April · Shift II]

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