Define F(x) as the product of two realfunctions f1(x)=x,x∈R, and f2(x)=sin⁡1/x; if x≠00; if x=0as follows F(x)=f1(x)f2(x);x≠00;x=0Statement-1: F(x) is continuous on RStatement-2: f1(x) and f2(x) are continuous on R.

Define F(x) as the product of two real

functions f1(x)=x,xR, and f2(x)=sin1/x; if x00; if x=0

as follows F(x)=f1(x)f2(x);x00;x=0

Statement-1: F(x) is continuous on R

Statement-2: f1(x) and f2(x) are continuous on R.

  1. A

    STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
     

  2. B

     STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for
    STATEMENT-1

  3. C

     STATEMENT-1 is True, STATEMENT-2 is False

  4. D

    STATEMENT-1 is False, STATEMENT-2 is True

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    Solution:

    Since |xsin1/x||x| so limx0F(x)=0=

    F(0) thus F is a continuous function. Since limx0sin1/x

    doesn’t exist so f2 is not continuous at x = 0.

     

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