Given the Fact That the Taylor Series About X = $e^{x}=1+\frac{x}{1 !}+\frac{x^{2}}{2 !}+\frac{x^{3}}{3 !}+\cdots$

question 57

True/False

Given the fact that the Taylor series about x = 0 for $e^{x}=1+\frac{x}{1 !}+\frac{x^{2}}{2 !}+\frac{x^{3}}{3 !}+\cdots$ , is the Taylor series about x = 0 for $e^{x / 4}=1+\frac{x}{4}+\frac{x^{2}}{32}+\frac{x^{3}}{384}+\cdots$ ?

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Definitions:

EPSPs

Excitatory Post-Synaptic Potentials, which are changes in cell membrane potential that make a neuron more likely to produce an action potential.

Potassium Channels

Protein structures in cell membranes that allow the passage of potassium ions through the membrane, critical for maintaining the cell's electrical stability.

Sodium Channels

Sodium channels are protein-based pores in cell membranes that allow sodium ions to pass through, playing a crucial role in the initiation and propagation of electrical signals in neurons.

Optogenetics

A biological technique that involves the use of light to control cells within living tissue, typically neurons, that have been genetically modified to express light-sensitive ion channels.