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
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Counter-Strike: Source (2004)
Duration: 2:56
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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 \( C \) is :
(a) 7
(b) \( \frac{3}{2} \)
(c) 2
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