Q. 95.0( 3 Votes )

Find which of the functions is continuous or discontinuous at the indicated points:


Answer :

Given,


…(1)


We need to check its continuity at x = 1


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 = 1 if -



Clearly,


LHL = {using equation 1}


LHL = (1-0)2/2 = 1/2 …(2)


Similarly, we proceed for RHL-


RHL = {using eqn 1}


RHL =


RHL =


RHL =


RHL = 2(0)2 + 0 + 1/2 = 1/2 …(3)


And,


f(1) = 12/2 = 1/2 {using eqn 1} …(4)


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



f(x) is continuous at x = 1


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