Find the First Four Non-Zero Terms of the Taylor Series $x e ^ { x }$

question 112

True/False

Find the first four non-zero terms of the Taylor series at x = 0 for f(x) = 1 + $x e ^ { x }$ .
Is $1 + x + x ^ { 2 } + \frac { x ^ { 3 } } { 2 ! }$ the correct answer?

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Definitions:

Discrete Probability Distributions

Probability distributions that characterize the outcomes of experiments with discrete outcomes, specifying the probability of each outcome.

Binomial Probabilities

The probabilities of obtaining a given number of successes in a fixed number of binary trials.

Normal Random Variable

A normal random variable is a variable whose values are subject to fluctuations according to a normal distribution.

Standard Deviations

A measure of the dispersion or variability in a dataset, indicating how much individual data points deviate from the mean.