Consider \( f(x)=x^{2}+a x+3 \) and \( g(x)=x+b \) and
\( \mathrm{P...
Consider \( f(x)=x^{2}+a x+3 \) and \( g(x)=x+b \) and
\( \mathrm{P} \) \( F(x)=\lim _{n \rightarrow \infty} \frac{f(x)+x^{2 n} g(x)}{1+x^{2 n}} \).
If \( F(x) \) is continuous at \( x=-1 \), then
(1) \( a+b=-2 \)
(2) \( a-b=3 \)
(3) \( a+b=5 \)
(4) none of these
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