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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
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.