Find the intervals on which \( f \) is increasing and the intervals on which it is decr \( f(x)=-\frac{x^{4}}{4}-2 x^{3}-4 x^{2} \) Select the correct choice and, if necessary, fill in the answer box(es) to comple

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

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.

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

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

\( \operatorname { Lim } _ { v \rightarrow + \infty } \frac { 6 e ^ { 2 v } - v ^ { 2 } + 1 } { e ^ { 2 v } - 4 \hat { u } + 1 } \)