RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 9. Continuity

Subject: Maths - Class 12th

Q. No. 10 of Exercise 9.1

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10

Discuss the continuity of the following functions at the indicated point(s).

at x = 1

In this problem we need to check continuity at x = a


Given function is


at x = 1 …… Equation 2


we need to check LHL, RHL and value of function at x = a (for idea and meaning of continuity refer to Q10(i) )


Clearly,


f(1) = n–1 [from equation 2]


LHL =


Using binomial theorem –


(1–h)n = 1 – nh + h2 – …….


LHL =


Putting h=0 we get,


LHL = n


RHL =


Using binomial expansion as used above we get the following expression


Similarly,


RHL =


Putting h=0 we get,


RHL = n


Thus RHL = LHL ≠ f(1)


f(x) is discontinuous at x=1


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