4)Encuentre las dimensiones del cilindro circular recto con volumen máximo que puede inscribirse en un cono circular recto de 8 pulgadas de radio y 12 pulgadas de altura

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

You go to the doctor and he gives you 12 milligrams of radioactive dye. After 24 minutes, 4.75 milligrams of dye remain in your system. To leave the doctor's office, you must pass through a radiation detector without sounding the alarm. If the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived? Give your answer to the nearest minute. You will spend minutes at the doctor's office.

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

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

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