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  • Solve! Which of the following statement is false ? ([.]= G.I.F)

Which of the following statement is false ? ([.]= G.I.F)

  • Option 1)

    f(x)= [x]  is continous from right at x=2

  • Option 2)

    f(x)= [\sin x]  is continous from right at x=-\pi/2

  • Option 3)

    f(x)= [\sin x]  is continous from right at x=\pi/2

  • Option 4)

    f(x)= x^{2}  is continous from right at x=2

 

Answers (1)

best_answer

As we have learned

Continuity from Right -

The function f(x) is said to be continuous from right at 

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

-

 

In (A),(B) and  (D) \rightarrow RHL = finite  value 

so (A),(B),(D) are true 

but in (C) \rightarrow RHL =0 ,f(\pi /2)  =1

\Rightarrow RHL \neq f(\pi /2)

f(x) =[sin x]  is not continous from right at x = \pi /2

 

 

 

 

 


Option 1)

f(x)= [x]  is continous from right at x=2

Option 2)

f(x)= [\sin x]  is continous from right at x=-\pi/2

Option 3)

f(x)= [\sin x]  is continous from right at x=\pi/2

Option 4)

f(x)= x^{2}  is continous from right at x=2

Posted by

Himanshu

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