\begin{tabular}{l} Question \\ Given \( F(x) \) below, find \( F^{\prime}(x) \). \( F(x)=\int_{x}^{5} \sqrt{2 t-2} d t \) \\ Provide your answer below: \\ \hline\( F^{\prime}(x)=\square \)\end{tabular}

\( \operatorname { Ard } d ( 6 t ^ { 5 } - t ^ { 3 } + 17 ) + ( 4 t ^ { 5 } + 7 t ^ { 3 } ) \)

b) \( \sum_{n=1}^{\infty} \sin \frac{\pi}{n^{2}} \)

\( \lim _ { n \rightarrow \infty } [ \frac { 1 } { \sqrt { 4 n ^ { 2 } - 1 } } + \frac { 1 } { \sqrt { 4 n ^ { 2 } - 2 ^ { 2 } } } + \cdots + \frac { 1 } { \sqrt { 3 n ^ { 2 } } } ] \)

\( \lim _{x \rightarrow \infty } (\frac{\arctan (x)e^{x^{1403}}}{1403+e^{x^{1403}}}) \)

At the beginning of an experiment, a scientist has 260 grams of radioactive goo. After 210 minutes, her sample has decayed to 8.125 grams. What is the half-life of the goo in minutes? 42 Find a formula for \( G(t) \), the amount of goo remaining at time \( t \). \( G(t)=260 e^{-0.0165 t} \) How many grams of goo will remain after 47 minutes? You may enter the exact value or round to 2 decimal places.