User:Gesalbte

Calculus

 * $$\int_{a}^{b} f(x)\,dx = F(b) - F(a).$$


 * $$\begin{align}

\lim_{m\rightarrow +\infty} P(1+{\frac{r}{m}})^{mt} & = \lim_{m\rightarrow +\infty} P{\frac{{[(m+r)^{mt}]}'}{{(m^{mt})}'}} \\ & = \lim_{m\rightarrow +\infty} P\dfrac{\dfrac{\operatorname{d}[(m+r)^m]^t}{\operatorname{d}[(m+r)^m]} \centerdot \dfrac{\operatorname{d}[(m+r)^m]}{\operatorname{d}(m+r)} \centerdot \dfrac{\operatorname{d}(m+r)}{\operatorname{d}m}}{\dfrac{\operatorname{d}(m^m)^t}{\operatorname{d}(m^m)} \centerdot \dfrac{\operatorname{d}m^m}{\operatorname{d}m}} \\ & = \lim_{m\rightarrow +\infty} P { \frac { t(m+r)^{(t-1)m} \centerdot (m+r)^m[1+\ln {(m+r)}] \centerdot (1+r) }

{t[m^{(t-1)m}] \centerdot m^m(1+\ln m)} } \\ & = \lim_{m\rightarrow +\infty} P(1+r) \\ & = P(1+r) \end{align}$$