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Limits from equations challenge

Problem

Let
f(x)={1+3cos(2x)if x<π4+sinxif xπ.\qquad f(x) = \begin{cases} 1+3\cos(2x) &\text{if $x<\pi$}\\ 4+\sin x &\text{if $x\geq \pi\,. $} \end{cases}
The limit, start subscript, x, \to, pi, end subscript, f, left parenthesis, x, right parenthesis is
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