Let $f(x, y)=y^{2}+3 y \int_{3}^{x} \sin \left(e^{t}\right) d t$ Find $f _ { x } ( 3,1 )$

question 12

Essay

Let $f(x, y)=y^{2}+3 y \int_{3}^{x} \sin \left(e^{t}\right) d t$ Find $f _ { x } ( 3,1 )$ and $f _ { y } ( 3,1 )$ to four decimal places.

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Definitions:

Sleeping Sickness

A parasitic disease transmitted by the tsetse fly, characterized by fever, headaches, joint pains, and sleep disturbances.

Incomplete Digestive Tract

A type of digestive system where a single opening serves as both mouth and anus, common in simpler organisms like cnidarians and flatworms.

Trachea

In insects, air tube located between the spiracles and the tracheoles. In tetrapod vertebrates, air tube (windpipe) that runs between the larynx and the bronchi.

Cephalothorax

A body region found in certain arthropods, including spiders and crustaceans, that combines the head and the thorax into one unit.