 ## 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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