A Taylor Polynomial Approximation Of $f ( x ) = e ^ { - \frac { x ^ { 2 } } { 2 } }$

question 58

Multiple Choice

A Taylor polynomial approximation of $f ( x ) = e ^ { - \frac { x ^ { 2 } } { 2 } }$ is given below. Use a graphing utility to graph both functions. $y = - \frac { 1 } { 2 } x ^ { 2 } + 1$

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Definitions:

Lowest Energy

Pertains to the state of a system in which it possesses the minimum possible energy, often corresponding to the most stable state.

Molecular Orbital

A theoretical construct that describes the wave-like behavior of electrons in molecules.

S-cis Conformation

A specific arrangement of molecular geometry where substituents on a double bond are positioned in the same plane, allowing potential for certain reactions.

Relative Energies

The comparative energy levels of molecules or states, used to predict stability, reactivity, and the distribution of products in chemical reactions.