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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 = 1–2sin2x
1–cos2x = 2sin2x
1–cos2x = 2sin2x
2k2
Since f(x) is continuous at x = 0 & f(0) = 8,then
2 k2 = 8
⇒ k2 = 4
⇒ k = ±2