Find the Principal Unit Normal Vector N for the Curve $r ( t ) = \left( t ^ { 2 } + 4 \right) \mathbf { j } + ( 2 t - 1 ) \mathbf { k }$

question 14

Multiple Choice

Find the principal unit normal vector N for the curve r(t) .
- $r ( t ) = \left( t ^ { 2 } + 4 \right) \mathbf { j } + ( 2 t - 1 ) \mathbf { k }$

• A) \(\mathbf { N } = - \frac { 1 } { \sqrt { \left( t ^ { 2 } + 1 \right) ^ { 3 } } } \mathbf { j } + \frac { t } { \sqrt { \left( t ^ { 2 } + 1 \right) ^ { 3 } } } \mathbf { k }\)
• B) \(\mathbf { N } = \frac { 1 } { \sqrt { \mathrm { t } ^ { 2 } + 1 } } \mathbf { j } - \frac { \mathrm { t } } { \sqrt { \mathrm { t } ^ { 2 } + 1 } } \mathbf { k }\)
• C) \(\mathbf { N } = - \frac { 1 } { \sqrt { t ^ { 2 } + 1 } } \mathbf { j } + \frac { \mathrm { t } } { \sqrt { \mathrm { t } ^ { 2 } + 1 } } \mathbf { k }\)
• D) \(\mathbf { N } = \frac { 1 } { \sqrt { \left( t ^ { 2 } + 1 \right) ^ { 3 } } } \mathbf { j } - \frac { \mathrm { t } } { \sqrt { \left( \mathrm { t } ^ { 2 } + 1 \right) ^ { 3 } } } \mathbf { k }\)

Identify the role of various emotions (e.g., anxiety, sadness, disgust) in influencing decisions and behaviors.

Understand how arousal levels (Yerkes-Dodson law) affect performance and concentration.

Learn about the concept of emotional intelligence and its importance in personal and professional contexts.

Acknowledge cultural and gender differences in emotional expressions and experiences.

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