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JEE Main 20209 JanuaryEvening Shift
Exam
JEE Main
Year
2020
Date
9 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Continuity and Differentiability

JEE Main 2020 · 9 January · Evening Shift · Mathematics · Continuity and Differentiability

Let [t] denote the greatest integer ≤ t and _ x → 0 x[(4)/(x)] = A...

Let [t]\left[t\right] denote the greatest integer ≤tandlim⁡x→0x[4x]=A.\le t and \lim_{x \to 0} x\left[\dfrac{4}{x}\right] = A . Then the function, f(x)=[x2]sin⁡(\pix)f\left(x\right) = \left[{x}^{2}\right]\sin \left(\pix\right) is discontinuous, when xx is equal to:

Options

  1. AA+1\sqrt{A + 1}
  2. BA+5\sqrt{A + 5}
  3. CA+21\sqrt{A + 21}
  4. DA\sqrt{A}

Correct answer

A. A+1\sqrt{A + 1}

Step-by-step solution

log⁡x→0(4x−{4x})=A⇒log⁡x→O4−x{4x}=A\log_{x \to 0} \left(\dfrac{4}{x} - \left\{\dfrac{4}{x}\right\}\right) = A ⇒ \log_{x \to O} 4 - x\left\{\dfrac{4}{x}\right\} = A

⇒4−0⇒ 4 - 0

⇒A=4⇒ A = 4

Hence, for 5\sqrt{5}, f(x)f\left(x\right) is discontinuous as it is an non-integral value.

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