Let $C$ Be a Smooth Curve Defined By $\mathbf { r } ( t ) = 7 \mathbf { i } + t \mathbf { j } + 4 t ^ { 2 } \mathbf { k }$

question 105

Short Answer

Let $C$ be a smooth curve defined by $\mathbf { r } ( t ) = 7 \mathbf { i } + t \mathbf { j } + 4 t ^ { 2 } \mathbf { k }$ , and let $\mathrm { T } ( t )$ and $\mathrm { N } ( t )$ be the unit tangent vector and unit normal vector to $C$ corresponding to $t$ . The plane determined by $\mathbf { T }$ and $\mathbf { N }$ is called the osculating plane. Find an equation of the osculating plane of the curve described by $\mathbf { r } ( t )$ at $t = 1$ .

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Definitions:

Repair Speed

The rate at which damaged or malfunctioning products or equipment are restored to working order.

Providing Redundancy

The act of incorporating extra components, systems, or processes to increase reliability and avoid failure in case of a component breakdown.

Backup

Backup refers to the process of copying and archiving computer data so it may be used to restore the original after a data loss event.

System Reliability

The probability that a system will perform its intended function adequately for a specified period under the given conditions.