A function is defined as \[ f(x)=\lim _{n \rightarrow \infty}\left\...

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A function is defined as
\[
f(x)=\lim _{n \rightarrow \infty}\left\{\begin{array}{ll}
\cos ^{2 n} x, & \text { if } x0 \\
\frac{1}{1+x^{n}}, & \text { if } 0 \leq x \leq 1 \\
\frac{1}{1+x^{n}}, & \text { if } x1
\end{array}\right.
\]
\( \mathrm{P} \)
W.
which of the following does not hold good?
(1) Continuous at \( x=0 \) but discontinuous at \( x=1 \)
(2) Continuous at \( x=1 \) but discontinuous at \( x=0 \)
(3) Continuous both at \( x=1 \) and \( x=0 \)
(4) Discontinuous both at \( x=1 \) and \( x=0 \)
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