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  Which of the following is true ?

  • Option 1)

    If f(x) is continous at 1 , f(1)= 10 then there exists an interval (1-\delta , 1+\delta )  such that \forall  

    x\epsilon (1-\delta ,1+\delta ) , f(x)= -5

  • Option 2)

    If f(x) is continous at 1 , f(1)= 10 then there exists an interval (1-\delta , 1+\delta )  such that \forall  

    x\epsilon (1-\delta ,1+\delta ) , f(x)= 1

  • Option 3)

    If f(x) is continous at 1 , f(1)= 10 then there exists an interval (1-\delta , 1+\delta )  such that \forall  

    x\epsilon (1-\delta ,1+\delta ) , f(x)> 0

  • Option 4)

    If f(x) is continous at 1 , f(1)= 10 then there exists an interval (1-\delta , 1+\delta )  such that \forall  

    x\epsilon (1-\delta ,1+\delta ) , f(x)< 0

 

Answers (1)

best_answer

As we have learned

Properties of Continuous function -

If  f is  continuous at a and  f(a)\neq 0   then there exists an open interval ( a-\delta ,\:a+\delta )   such that for all  x\epsilon  (a-\delta ,\:a+\delta )  f(x)   has the same sign as  f(a)

-

 

 If f(x) is continous  at x= a, f(a) \neq zero than there exists an interval (a-\delta ,a+\delta ) such that \forall n\epsilon (a-\delta ,a+\delta ), f(x) has same sign ad f(a)

 

 

 

 


Option 1)

If f(x) is continous at 1 , f(1)= 10 then there exists an interval (1-\delta , 1+\delta )  such that \forall  

x\epsilon (1-\delta ,1+\delta ) , f(x)= -5

Option 2)

If f(x) is continous at 1 , f(1)= 10 then there exists an interval (1-\delta , 1+\delta )  such that \forall  

x\epsilon (1-\delta ,1+\delta ) , f(x)= 1

Option 3)

If f(x) is continous at 1 , f(1)= 10 then there exists an interval (1-\delta , 1+\delta )  such that \forall  

x\epsilon (1-\delta ,1+\delta ) , f(x)> 0

Option 4)

If f(x) is continous at 1 , f(1)= 10 then there exists an interval (1-\delta , 1+\delta )  such that \forall  

x\epsilon (1-\delta ,1+\delta ) , f(x)< 0

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Himanshu

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