[tex] \\ A) \:\ \:\ f'_{(x)} = (3x+e^x)' = 3 + e^x , x \in \mathbb{R}
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\\ B) \:\ \lim _{x\to \:-\infty \:}\left(\frac{3x+e^x}{x}\right) =\lim _{x\to \:-\infty \:}\left(3+\frac{e^x}{x}\right) =>
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\\ \lim _{x\to \:-\infty \:}\left(3\right)+\lim _{x\to \:-\infty \:}\left(\frac{e^x}{x}\right) => 3+0 = \boxed{3} [/tex]
