Let \( g(x)=x^{C} e^{C x} \) and \( f(x)=\int_{0}^{x} t e^{2 t}\left(1+3 t^{2}\right)^{1 / 2} d ...

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Counter-Strike: Source
Game:
Counter-Strike: Source (2004)
Duration: 2:54
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Let \( g(x)=x^{C} e^{C x} \) and \( f(x)=\int_{0}^{x} t e^{2 t}\left(1+3 t^{2}\right)^{1 / 2} d t \). If \( L=\lim _{x \rightarrow \infty} \frac{f^{\prime}(x)}{g^{\prime}(x)} \) is non-zero finite number then :
The value of \( L \) is :
(a) \( \frac{2}{7} \)
(b) \( \frac{1}{2} \)
(c) \( \frac{\sqrt{3}}{4} \)
(d) \( \frac{\sqrt{3}}{2} \)
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