Find the First Four Non-Zero Terms of the Taylor Series $f ( x ) = \sin 2 x$

question 108

True/False

Find the first four non-zero terms of the Taylor series at x = 0 of $f ( x ) = \sin 2 x$ .
Is $f ( x ) = 2 x - \frac { 8 x ^ { 3 } } { 3 ! } + \frac { 32 x ^ { 5 } } { 5 ! } - \frac { 128 x ^ { 7 } } { 7 ! }$ the correct answer?

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Definitions:

Variables

Elements, features, or factors that are likely to vary or change within the context of a scientific study or experiment.

Correlation Coefficients

Statistical measures that indicate the extent to which two or more variables fluctuate together, ranging from -1 to 1, where 1 indicates a perfect positive correlation and -1 indicates a perfect negative correlation.

Cause and Effect

A relationship between events or things, where one is the result of the other or others, a combination of action and reaction.

Negatively Correlated

Describes a relationship between two variables where one variable increases as the other decreases.