Find Parametric Equations for the Tangent Line to the Curve $$x = \cos t , y = 2 e ^ { 6 t } , z = 2 e ^ { - 6 t } ; ( 1,2,2 )$$

question 133

Multiple Choice

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. Select the correct answer.
$$x = \cos t , y = 2 e ^ { 6 t } , z = 2 e ^ { - 6 t } ; ( 1,2,2 )$$

• A) \(x = t , y = 2 - 24 t , z = 2 + 24 t\)
• B) \(x = 1 , y = 2 - 24 t , z = 4 - 24 t\)
• C) \(x = 1 , y = 2 + 12 t , z = 2 - 12 t\)
• D) \(x = 0 , y = 2 - 24 t , z = 2 + 24 t\)
• E) \(x = t , y = 2 + 12 t , z = 2 - 12 t\)

---

Definitions:

Inner Lives

The complex internal experiences and emotional life of an individual.

Corvids

A family of birds that includes ravens, crows, jays, and magpies, known for their high intelligence and complex social behaviors.

Hominins

Members of the human lineage, including modern humans, Homo sapiens, and our closest ancestors and relatives, after diverging from the lineage of chimpanzees.

Corrective Lenses

Optical appliances designed to correct or enhance vision, including glasses and contact lenses.