A company manufactures and sells \( x \) clocks per week with weekly price-demand function: \( f(p)=30-3 p \) where \( p \) is the price per clock. a. Compute the elasticity of demand function, \( E(p) \), for this demand function. \( E(p)= \) b. At \( p=3 \), a price increase of \( 2 \% \) will create a demand decrease of what percent? Round to 2 decimal places if necessary.

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.

\( \int \cosh ^ { 2 } ( x - 3 ) \sinh ( x - 3 ) d x \)

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

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

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