Which of the following is true ?

  • Option 1)

    f(x)= 1/|x|   is continous at x= 0

  • Option 2)

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

  • Option 3)

    f(x)= [x]   is continous at x= 1([.]=G.I.F)

  • Option 4)

    f(x)= [x]   is continous at x= 1.5([.]= G.I.F)

 

Answers (1)
H Himanshu

As we have learned

Continuity at a point -

A function f(x)  is said to be continuous at  x = a in its domain if 

1.  f(a) is defined  : at  x = a.

2. \lim_{x\rightarrow a}\:f(x)\:exists\:means\:limit\:x\rightarrow a

of  f(x) at  x = a exists from left and right.

3. \lim_{x\rightarrow a}\:f(x)=f(a)\:then\:the\:limit\:equals \:the\:value\:at\:x=a

-

 

 In(A) , f(x) is not defined at x=0

In (B) , f(x) is not defined at x=0 and also LHL\neqRHL

In (C) , f(x) is defined at  x= 1, f(1) =1

But f(1) LHL, RHL all are not same 

In (D) f(1.5)= f(1.5^{+})= f(1.5^{-})=0

 

 


Option 1)

f(x)= 1/|x|   is continous at x= 0

Option 2)

f(x)= |x|/x   is continous at x= 0

Option 3)

f(x)= [x]   is continous at x= 1([.]=G.I.F)

Option 4)

f(x)= [x]   is continous at x= 1.5([.]= G.I.F)

Exams
Articles
Questions