$$\lim _\limits{n \rightarrow \infty}\left(\frac{1}{1^5+n^5}+\frac{2^4}{2^5+n^5}+\frac{3^4}{3^5+n^5}+\ldots+\frac{n^4}{n^5+n^5}\right)=$$

If $$\lim _\limits{x \rightarrow 0}\left(\frac{11 x^3-3 x+4}{13 x^3-5 x^2-7}\right)=\frac{a}{b}$$, then the value of $$a+b$$ equals

$$\lim _\limits{x \rightarrow 1} \frac{(1-x)\left(1-x^2\right) \ldots\left(1-x^{2 n}\right)}{\left\{(1-x)\left(1-x^2\right) \ldots \ldots\left(1-x^n\right)\right\}^2}= $$ _____________, $$\forall n \in N$$

If $$f(x)=\frac{\log _e\left(1+x^2(\tan x)\right)}{\sin x^3}, x \neq 0$$ is to be continuous at $$x=0$$, then $$f(0)$$ must be equal to