Discuss the continuity of the function :...

Discuss the continuity of the function :
`f(x)={{:((|x-a|)/(x-a)",when "xnea),(1" ,when "x=a):}` at x = a.

A

f(x) is continous at x=a

B

f(x) is discontinuous at x=a

C

`lim_(xtoa)f(x)=1`

D

None of these

Verified by Experts

The correct Answer is:

B

Similar Questions

Explore conceptually related problems

Discuss the continuity of the function : f(x)={{:((|x-2|)/(x-2)", "xne2),(1" ,"x=2):} at x = 2

Discuss the continuity of the function f given f(x)=|x| at x=0

Discuss the continuity of the function : f(x)={{:((|x-2|)/(2-x)", "xne2),(-1" ,"x=2):} at x = 2

Discuss the continuity of the function f(x)={((|x|)/x", " xne 0),(1", " x=0):} at x=0

Discuss the continuity of the function f defined f(x)=(1)/(x),x!=0

Discuss the continuity of the function (x)/(|x|),x!=00,x=0

Discuss the continuity of f(x) =[x]

Discuss the continuity of the function : f(x)={{:((1-cosx)/x^(2)", "xne0),(1", "x=0):} at x = 0.

Discuss the continuity of the function = f(x) ={(3-x", "x le 0),(x", "x gt 0):} at x=0.