Find the Unit Tangent Vector T(t) to the Curve R $t \mathbf { i } + t ^ { 2 } \mathrm { j }$

question 105

Multiple Choice

Find the unit tangent vector T(t) to the curve r (t) = $t \mathbf { i } + t ^ { 2 } \mathrm { j }$ when t = 0.

• A)i
• B)j
• C) \(\frac { 1 } { \sqrt { 2 } } \mathbf { i } + \frac { 1 } { \sqrt { 2 } } \mathbf { j }\)
• D) \(\frac { 1 } { \sqrt { 2 } } \mathbf { i } - \frac { 1 } { \sqrt { 2 } } \mathbf { j }\)
• E) \(\frac { 2 } { \sqrt { 5 } } \mathbf { i } + \frac { 1 } { \sqrt { 5 } } \mathbf { j }\)
• F) \(\frac { 1 } { \sqrt { 5 } } \mathbf { i } + \frac { 2 } { \sqrt { 5 } } \mathbf { j }\)
• G) \(\frac { 2 } { \sqrt { 5 } } \mathbf { i } - \frac { 1 } { \sqrt { 5 } } \mathbf { j }\)
• H) \(\frac { 1 } { \sqrt { 5 } } \mathbf { i } - \frac { 2 } { \sqrt { 5 } } \mathbf { j }\)

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Definitions:

American Law Institute (ALI) Rule

A legal standard for insanity that assesses whether a defendant lacked the capacity to understand the wrongfulness of their actions or conform their conduct to the law due to mental illness.

M'Naghten Rule

A legal principle that excuses a defendant from liability if at the time of the crime, they were suffering from a mental illness that prevented them from understanding the nature of their actions or knowing right from wrong.

Durham Rule

A legal standard used to determine insanity, stating that an accused is not criminally responsible if the unlawful act was the product of mental disease or defect.

Act of Passion

Refers to an action taken in a moment of intense emotion, especially love or anger, that is not premeditated.