Provide an Appropriate Response $\mathrm { P } _ { 0 }$

question 121

Multiple Choice

Provide an appropriate response.
-Find the direction in which the function is increasing most rapidly at the point $\mathrm { P } _ { 0 }$ . $f ( x , y , z ) = x y - \ln ( z ) , P _ { 0 } ( 1,2,2 )$

• A) \(\frac { 1 } { 21 } ( 4 \mathrm { i } + 2 \mathrm { j } - \mathrm { k } )\)
• B) \(\frac { 1 } { \sqrt { 21 } } ( 4 i - 2 j + k )\)
• C) \(\frac { 21 } { \sqrt { 21 } } ( 4 i + 2 j - k )\)
• D) \(\frac { 1 } { \sqrt { 21 } } ( 4 i + 2 j - k )\)

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Definitions:

Molecule

The smallest particle in a chemical element or compound that has the chemical properties of that element or compound.

Covalent Bonds

Chemical bonds formed by the sharing of electron pairs between atoms.

Electronegativity

Electronegativity is a chemical property that describes the tendency of an atom to attract electrons towards itself in a chemical bond.

Valence Bond Theory

A theory that explains how electrons are shared between atoms to form chemical bonds, focusing on the concept of hybridization of atomic orbitals.