Answer :

Given,


…(1)


We need to check its continuity at x = 4


A function f(x) is said to be continuous at x = c if,


Left hand limit(LHL at x = c) = Right hand limit(RHL at x = c) = f(c).


Mathematically we can represent it as-



Where h is a very small number very close to 0 (h0)


Now according to above theory-


f(x) is continuous at x = 4 if -



Clearly,


LHL = {using equation 1}


LHL =


h > 0 as defined above.


|-h| = h


LHL =


LHL = -1/2 …(2)


Similarly, we proceed for RHL-


RHL = {using equation 1}


RHL =


h > 0 as defined above.


|h| = h


RHL =


RHL = 1/2 …(3)


And,


f(4) = 0 {using eqn 1} …(4)


Clearly from equation 2 , 3 and 4 we can say that



f(x) is discontinuous at x = 4


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