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
