(b) Determine the modulus and argument of \( c^{5} \), where \( c=1+i \sqrt{3} \). \( \quad \begin{array}{c}c^{2}=1+i \sqrt{3} \\ c^{5}=1+\end{array} \) (c) Show that \( \int_{C} \exp \left(\frac{1}{z^{2}}\right)=0 \) where \( C \) is the unit circle \( |z|=1 \)

\( \lim _ { x \rightarrow 2 } \frac { x ^ { 3 } - x ^ { 2 } + 2 x - 4 } { x ^ { 2 } + 3 x - 10 } = \frac { 0 } { 0 } \quad F \)

\( \begin{array}{ll}\text { (2) } \int \frac{d x}{7-3 x} & \text { (3) } \int \sqrt[3]{x+5} d x \\ \text { (5) } \int \frac{d x}{(2 x-5)^{2}} & \text { (6) } \int \sqrt[3]{(5-3 x)^{2}} d x\end{array} \)

\[ \frac{n!}{n^{n}} \leq \frac{1}{2^{n-1}}, \quad \forall n \in \mathbb{N}, \quad \text { dopo aver dimostrato per induzione la validità della disuguaglianza } \] verificare che la successione \( a_{n}=\frac{n!}{n^{n}} \) converge a zero.

Using Fundamental Theorem of Calculus: Part One, find the following: 1. Given \( f(t)=\left(2+t^{4}\right)^{5} \) and \( g(x)=\int_{1}^{x}\left(2+t^{4}\right)^{5} d t \), what is \( g^{\prime}(x)= \) ?

\( \frac { ( n + 1 ) ! } { ( n + 1 ) ^ { n + 1 } } \leq \frac { 1 } { 2 ^ { n } } \)