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  • Help me solve this Which of the following statement is false ?

Which of the following statement is false ?

  • Option 1)

    f(x)= \sin x  is left continous at x= \pi /2

  • Option 2)

    f(x)= [ x]  is left continous at x= 2

  • Option 3)

    f(x)= |x|  is left continous at x= 0

  • Option 4)

    f(x)= [x^{2}]  is left continous at x= 0

 

Answers (1)

best_answer

As we have learned

Continuity from Left -

The function f(x) is said to be continuous from left at x = a if 

\lim_{x\rightarrow a^{-}}\:f(x)=f(a)

-

 

 To check left continuity we need to find LHL and funtion value at the point x=a

(A)\rightarrow LHL =1, f(\pi /2)=1;

(B)\rightarrow LHL =1, f(2)=2;

(C)\rightarrow LHL =0, f(0)=0;

(D)\rightarrow LHL =0, f(0)=0

f(x)=[x] is not continous at x=2

 


Option 1)

f(x)= \sin x  is left continous at x= \pi /2

Option 2)

f(x)= [ x]  is left continous at x= 2

Option 3)

f(x)= |x|  is left continous at x= 0

Option 4)

f(x)= [x^{2}]  is left continous at x= 0

Posted by

Himanshu

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