Find the Unit Tangent Vector T(t) to the Curve R $\left( \sin t , 2 t , t ^ { 2 } \right)$

question 106

Multiple Choice

Find the unit tangent vector T(t) to the curve r (t) = $\left( \sin t , 2 t , t ^ { 2 } \right)$ when t = 0.

• A) \(\left( - \frac { 2 } { \sqrt { 5 } } , - \frac { 1 } { \sqrt { 5 } } , 0 \right)\)
• B) \(\left( \frac { 2 } { \sqrt { 5 } } , - \frac { 1 } { \sqrt { 5 } } , 0 \right)\)
• C) \(\left( - \frac { 2 } { \sqrt { 5 } } , \frac { 1 } { \sqrt { 5 } } , 0 \right)\)
• D) \(\left( \frac { 2 } { \sqrt { 5 } } , \frac { 1 } { \sqrt { 5 } } , 0 \right)\)
• E) \(\left( - \frac { 1 } { \sqrt { 5 } } , - \frac { 2 } { \sqrt { 5 } } , 0 \right)\)
• F) \(\left( \frac { 1 } { \sqrt { 5 } } , - \frac { 2 } { \sqrt { 5 } } , 0 \right)\)
• G) \(\left( - \frac { 1 } { \sqrt { 5 } } , \frac { 2 } { \sqrt { 5 } } , 0 \right)\)
• H) \(\left( \frac { 1 } { \sqrt { 5 } } , \frac { 2 } { \sqrt { 5 } } , 0 \right)\)

---

Definitions:

Total Revenue

The combined sum of earnings a company receives for its goods sold and services rendered over a particular time span.

Standardized Product

Goods or services that are uniform in quality and performance, allowing them to be interchangeable.

Perfect Competition

A market structure characterized by a large number of small firms, identical products, and ease of entry and exit, leading to no single firm influencing the market price.

Many Buyers

A market condition where there are numerous consumers for a product, enhancing competition and potentially reducing prices.