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Find k that value of the function in the interval is continuousf(x)= k cos x, x<=0 2x -k, x>0 |
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Answer» f(x) \(=\begin{cases}k\,cos\,x;&x\leq0\\2^x-k;&x>0\end{cases}\) f(0-) \(=\underset{x\rightarrow0}{Lim}\) k cos x = k cos 0 = k f(0+) \(=\underset{x\rightarrow0}{Lim}\) 2x - k = 20 - k = 1 - k ∵ f(x) is continuous at x = 0 ∴ f(0-) = f(0+) ⇒ k = 1 - k ⇒ 2k = 1 ⇒ k = 1/2. |
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