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Question

Let [t] denotes the greatest integer t and limx0x4x=AThen the function, f(x)=[x2]sinπx is discontinuous, when x is equal to:


A

(A+1)

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B

A

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C

(A+5)

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D

(A+21)

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Solution

The correct option is A

(A+1)


Explanation for The correct option:

Finding the required value of x

The given function f(x)=[x2]sinπx

It is continuous xZ as sinπx as is continuous at Z.

So, the function f(x) is discontinuous at points where[x2] is discontinuous i.e. x2Z is an exception point that f(x) is continuous as x is an integer.

Therefore, the points of discontinuity for f(x) be

x=±2,±3,±5,

And given that

limx0x4x=A

We get indeterminate form of (0×)

Therefore,

4limx04x=A Since x is a greatest integer function

A=4(A+5)=3(A+1)=5

thus the points of discontinuity for the function is (A+1)

Hence, the correct option is (A)


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