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  • Try this! - Limit , continuity and differentiability - JEE Main-7

Let f(x) = \sin x   \forall x\epsilon e   and g(x) = \cos x   \forall x\epsilon R  

 then which of the following is not conitnous \forall n\epsilon R  ?   

  • Option 1)

    f(x)+g(x)

  • Option 2)

    f(x)-g(x)

  • Option 3)

    f(x)*g(x)

  • Option 4)

    f(x)/g(x)

 

Answers (1)

best_answer

As we have learned

Properties of Continuous function -

If   f,\:g   are two continuous functions at a point a of their common domain D.Then  f\pm g   fg are continuous at  a  and if   g(a)\neq 0  then 

 \frac{f}{g}      is also continuous at  x = a.

-

 

\because f(x)=\sin x,g(x)= \cos x qare continous foa all  n\epsilon R

\therefore f(x) \pm g(x)  and  \therefore f(x)\cdot g(x)  will be discontinous whenever g(x)=0 , so there are various x in (-\infty ,\infty ) such that g(x)= cos x=0

\therefore \frac{f(x)}{g(x)}  is not continous throughout 

 

 

 

 

 


Option 1)

f(x)+g(x)

Option 2)

f(x)-g(x)

Option 3)

f(x)*g(x)

Option 4)

f(x)/g(x)

Posted by

Himanshu

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