f(x)=[x]+[-x] when xis not equal to 2 and A ,when X =2 if fx is continuous at x=2 thwn the value of A=?

3 years ago

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Answers : (2)

                                        

Hi Koushik,


 


Ih you note


f(x) as x tends to 2 from the right ie 2+


f(2+) = 2-3 = -1


And f(x) as x tends to 2 from the left ie 2-


f(2-) = 1-2 = -1.


 


So f(2) = A = -1 for f(x) to be continuous at 2.


 


Hope it helps.


Wish you all the best.


 


Regards,


Ashwin (IIT Madras).

3 years ago
                                        

For continuity lim x->2+ f(x) = f(2) = lim x-> 2-


Evalutaing left hand limit: 


When x->2-: [x]+[-x] = [2-h]+[-(2-h)] =1+[-2+h]=1-2=-1


Evaluating right hand limit


When x->2+ : [2+h]+[-2-h]= 2+(-3)= -1 


therefore f(2) = -1 to mk the function continuous

3 years ago

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