Q. 14.3( 8 Votes )

Examine the continuity of the function

f(x) = x3 + 2x – 1 at x = 1

Answer :

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) = x3 + 2x – 1 is continuous at x = 1 if -



Clearly,


LHL =


LHL = (1-0)3 + 2(1-0) – 1 = 2 …(1)


Similarly, we proceed for RHL-


RHL =


RHL = (1+0)3 + 2(1+0) – 1 = 2 …(2)


And,


f(1) = (1+0)3 + 2(1+0) – 1 = 2 …(3)


Clearly from equation 1 , 2 and 3 we can say that



f(x) is continuous at x = 1


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