Answer :

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

Rate this question :

If Find whether f(x) is continuous at x = 0.

RD Sharma - Volume 1Find which of the functions is continuous or discontinuous at the indicated points:

at x = 4

Mathematics - ExemplarDiscuss the continuity of the following functions at the indicated point(s).

at

x = a

Find which of the functions is continuous or discontinuous at the indicated points:

at x = 0

Mathematics - ExemplarFind which of the functions is continuous or discontinuous at the indicated points:

at x = 2

Mathematics - ExemplarIf is continuous at then

Mathematics - Exemplarat x = 0

Mathematics - ExemplarFind the value of k so that the function f is continuous at the indicated point:

Mathematics - Exemplar