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 & f(0) = 8

If f(x) to be continuous at x = 0,then,

f(0)^{–} _{=} f(0) ^{+ =} f(0)

LHL = f(0)^{–} =

cos(–x) = cosx

cos2x = 1–2sin^{2}x

1–cos2x = 2sin^{2}x

1–cos2x = 2sin^{2}x

2k^{2}

Since f(x) is continuous at x = 0 & f(0) = 8,then

2 k^{2} = 8

⇒ k^{2} = 4

⇒ k = ±2

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