RD Sharma - Mathematics (Volume 1)

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


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