Compute the Gradient of the Function at the Given Point $$f ( x , y , z ) = \ln \left( x ^ { 2 } + 5 y ^ { 2 } - 7 z ^ { 2 } \right) , \quad ( 5,5,5 )$$

question 71

Multiple Choice

Compute the gradient of the function at the given point.
- $$f ( x , y , z ) = \ln \left( x ^ { 2 } + 5 y ^ { 2 } - 7 z ^ { 2 } \right) , \quad ( 5,5,5 )$$

• A)\({\nabla} f = - i - 2 j + \frac { 10 } { 7 } \mathbf { k }\)
• B)\({\nabla} f = - \frac { 2 } { 5 } \mathbf { i } - 2 \mathbf { j } + \frac { 14 } { 5 } \mathbf { k }\)
• C)\({\nabla} f = - \frac { 2 } { 5 } \mathbf { i } - 2 \mathbf { j } + \frac { 10 } { 7 } \mathbf { k }\)
• D)\({\nabla} f = - \mathrm { i } - 2 \mathrm { j } + \frac { 14 } { 5 } \mathbf { k }\)

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Definitions:

Gastric Motility

The movements of the stomach muscles that mix and propel contents through the gastrointestinal tract.

Enteric Plexus

A network of neurons located in the gastrointestinal tract walls that helps regulate the digestive process.

Submucosal Plexus

Gangliated plexus of unmyelinated nerve fibers in the intestinal submucosa.

Myenteric Plexus

Part of the nervous system in the gastrointestinal tract that controls gut movement and function.