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

(a^{3}–b^{3}) = (a–b)(a^{2} + ab + b^{2})

∴ 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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