Find Parametric Equations for the Tangent Line to the Curve $x = t ^ { 11 } , y = t ^ { 5 } , z = t ^ { 6 } ; ( 1,1,1 )$

question 129

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.
$x = t ^ { 11 } , y = t ^ { 5 } , z = t ^ { 6 } ; ( 1,1,1 )$

• A) \(x = 11 t , y = 1 + 5 t , z = 1 + 6 t\)
• B) \(x = 1 + 11 t , y = 1 + 5 t , z = 1 - 6 t\)
• C) \(x = 1 + 11 t , y = 1 + 5 t , z = 1 + 6 t\)
• D) \(x = 1 + 11 t , y = 1 - 5 t , z = 1 + 6 t\)
• E) \(x = 1 - 11 t , y = 1 + 5 t , z = 1 + 6 t\)

---

Definitions:

Parental Attitudes

Refers to the feelings, beliefs, and behaviors that parents have towards their offspring which significantly impact their development.

Style of Life

An individual's unique set of behaviors, attitudes, and habits that are developed to navigate life and achieve personal goals.

Alcoholics

People suffering from alcoholism, which is a chronic disease characterized by uncontrolled drinking and preoccupation with alcohol.

Drug Addicts

Individuals who suffer from a dependence on substances, leading to compulsive drug seeking and use despite harmful consequences.