Questions on the evaluation of derivatives or problems involving derivatives (for example, use of the mean value theorem).

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Is this proof that $g$ is continuous correct?

I have proved that $g$ is continuous on $(0,2)$ and I just wish to check if my solution for $g$ being right continuous at $0$ and hence continuous at $0$ is correct. $$\lim\limits_{x \to 0^+}g(x) ...
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Analyze the variation of this function $f(x)=x \exp[a+b(x-1)] \, E_1[a+b (x-1)]$ w.r.t. $x$

Please, I need to analyse the variation of the following function w.r.t. $x$ : $f(x)=x \exp[a+b(x-1)] \, E_1[a+b (x-1)]$, where $E_1[a+b (x-1)]$ is the exponential integral, $b>a$, $a>0$, ...