Book: RD Sharma - Mathematics (Volume 1)
Chapter: 9. Continuity
Subject: Maths - Class 12th
Q. No. 44 of Exercise 9.1
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44
Let 
. If f(x) is continuous at
find a and b.
Given:
f(x) is continuous at x = 
& f(
) = a,
If f(x) to be continuous at x = 
,we have to show, f(
)– = f(
) + = f(
)
LHL = f(
)– = 
sin(
–x) = cosx
cos(
–x) = sinx
(a3–b3) = (a–b)(a2 + ab + b2)
∴ cos(0) = 1
...(1)
LHL = f(
) + =
1
...(2)
f(x) is continuous at x = 
& f(
) = a ,and from (1) & (2),we get
f(
)– = f(
) + = f(
)
= a
a = 
⇒ b = 4
Hence ,a = 
& b = 4
