Find the Equation for the Plane Tangent to the Parametrized

question 90

Essay

Find the equation for the plane tangent to the parametrized surface S at the point P.
- $$\mathrm { S } \text { is the paraboloid } r ( \theta , r ) = r \cos \theta i + r \sin \theta j + 5 r ^ { 2 } \mathbf { k } ; \mathrm { P } \text { is the point corresponding to } ( \theta , r ) = \left( \frac { \pi } { 4 } , 1 \right) \text {. }$$

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Definitions:

Statistical Stability

The property of a statistical measure to remain constant over time or across different samples.

Special Causes

Unusual, not predictable factors in a process that can cause variations and are not part of the process itself.

Common Cause Variation

Variation that is inherent in a process over time, caused by factors that are consistently and predictably present.

Control Charts

Visual tools used in statistical process control to monitor how a process changes over time, highlighting variations outside of predefined bounds.