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The principal part of

e^{3}-e^{x^{3}+3}

x \rightarrow 0

is a.

1-e^{3}

...

Jan 30, 2024

The principal part of

e^{3}-e^{x^{3}+3}

x \rightarrow 0

is a.

1-e^{3}

-\frac{x^{3}}{e^{3}}

-e^{3} x^{3}

-e^{3} x

Solution by Steps

step 2

The Taylor series expansion of

e^{x^3+3}

x=0

is given by

e^3 - e^3 x^3 - \frac{e^3 x^6}{2} - \frac{e^3 x^9}{6} + O(x^{11})

step 3

The principal part of the series is the term with the lowest degree of

x

that is not a constant. In this case, it is

-e^3 x^3

Key Concept

Principal Part of a Series

Explanation

The principal part of a series is the term with the lowest degree of the variable that is not a constant, which represents the most significant part of the series as the variable approaches zero.