QJEEM20Maf05c: JEE Main 2020 Mathematics - Class 12 JEEM20Maf05c Solution: Let [t] denote the greatest integer ≤ t and lim x → 0 ⁡ x [ 4 x …

Question

Verified Solution • 2025–26 Session moderate

Let [t] denote the greatest integer

\leq

t and

lim_{x \to 0} x [\frac{4}{x}] = A

.
Then the function, f(x) = [x²]sin(

π

x) is discontinuous, when x is equal to :

Accepted Answer

A =

lim_{x \to 0} x [\frac{4}{x}]

=

lim_{x \to 0} x (\frac{4}{x} - {\frac{4}{x}})

=

lim_{x \to 0} (4 - {\frac{4}{x}})

= 4

Now, when x =

\sqrt{A + 1}

=

\sqrt{5}

, f(x) = [x²]sin(

π

x) is discontinuous at this non integer point.

But at x = 2, 3 and 5, f(x) is continuous.

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