If f(x) ={((x-|x|)/x,",","when"x != 0),(...

If `f(x) ={((x-|x|)/x,",","when"x != 0),(2,",","when"x = 0):}` , then

A

(a) f(x) is continuous at x = 0

B

(b) f(x) is discontinuous at x = 0

C

(c) `lim_(x to 0)f(x) = 2`

D

(d) `lim_(x to 0^(-))f(x) = lim_(x to 0^(+))f(x)`

Verified by Experts

The correct Answer is:

B

Similar Questions

Explore conceptually related problems

If f(x) ={(e^(1/x),",","when"x != 0),(1,",","when"x = 0):} , then

If f(x)={(x^(2)(sin)1/x,",","when" x != 0),(0,",","when"x = 0):} , then

If f(x) = {(x^(2), ",","when" x != 1),(2,",","when" x = 1):} , then

If f(x)={((1)/(e^(1/x)+1),",","when" x != 0),(0,",","when"x = 0):} , then

If f(x) = {((|x-a|)/(x-a), ",","when"x != a),(1, ",", "when"x = a ):} , then

If f(x) ={((x^(4)-16)/(x-2),",","when"x != 2),(16,",","when"x = 2):} , then

If f(x) = {((sin 2x)/(5x), ",", "when" x != 0),(k, ",", "when" x = 0):} is continuous at x = 0, then the value of k will be

If f(x) = {(x^(2), ",","when" x le 1),(x+5,",","when" x gt 1):} , then

If {:(f(x),=(|x|)/(x),",","for" x != 0),(,=1, ",","for" x = 0):} , then f(x) is

If f(x) = {(1+x^(2),",", "when"0 le x lt 1),(1-x,",","when"x gt 1):} , then