$\mathop {\lim }\limits_{n \to \infty } \left[ {\frac{{{1^3} + {2^3} + {3^3} + \dots + {n^3}}}{{{n^4}}}} \right] = $

If $\lim _{x \rightarrow 0} \frac{\left(e^{k x}-1\right) \sin k x}{x^{2}}=4$,then $k$ is equal to

$\lim _{n \rightarrow \infty} P\left(1+\frac{r}{100 n}\right)^{t n} =$

Let $f(x) = \frac{\ln(x^2 + e^x)}{\ln(x^4 + e^{2x})}$. If $\lim_{x \to \infty} f(x) = l$ and $\lim_{x \to -\infty} f(x) = m$,then:

If $\lim_{n \rightarrow \infty} \frac{(n+1)^{k-1}}{n^{k+1}}[(nk+1)+(nk+2)+\ldots+(nk+n)] = 33 \cdot \lim_{n \rightarrow \infty} \frac{1}{n^{k+1}} \cdot [1^k + 2^k + 3^k + \ldots + n^k]$,then the integral value of $k$ is equal to $....$

If $f(x) = \frac{1-x+\sqrt{9x^2+10x+1}}{2x}$,then $\lim_{x \rightarrow -1^{-}} f(x) = $