Let \( f(x)=\left\{\begin{array}{cc}x g(x) & , x \leq 0 \\ x+a x^{2...

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Let \( f(x)=\left\{\begin{array}{cc}x g(x) & , x \leq 0 \\ x+a x^{2}-x^{3}, & x0\end{array}\right. \), where \( g(t)=\lim _{x \rightarrow 0} \)
P \( (1+a \tan x)^{t x} \), a is positive constant, then Set of all values of a for which function \( f(x) \) is continuous at \( \mathrm{x}=0 \)
(a) \( (-1,10) \)
(b) \( (-\infty, \infty) \)
(c) \( (0, \infty) \)
(d) none of these
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