In each of the following, find the value of the constant k so that the given function is continuous at the indicated point :

at x = 0

Given:

f(x) is continuous at x = 0

If f(x) to be continuous at x = 0,thenf(0)^{–} _{=} f(0) ^{+ =} f(0)

RHL = f(0)^{–} =

cos(0) = 1

f(0) ^{+}

LHL = f(0)^{–} =

⇒ k×0

⇒ 0

Hence, the value of k = 0.

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