Use Series to Evaluate the Limit $\lim _ { x \rightarrow 0 } \frac { \tan ^ { - 1 } 10 x - \tan 10 x } { x ^ { 3 } }$

question 427

Multiple Choice

Use series to evaluate the limit.
- $\lim _ { x \rightarrow 0 } \frac { \tan ^ { - 1 } 10 x - \tan 10 x } { x ^ { 3 } }$

• A) \(- 150\)
• B) \(- \frac { 2000 } { 3 }\)
• C) \(- \frac { 1000 } { 3 }\)
• D) \(- \frac { 100 } { 3 }\)

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Definitions:

Significance Level

A threshold chosen by the researcher which the p-value must be below in order to reject the null hypothesis.

Explanatory Variables

Variables in a statistical model that are used to predict or explain changes in the dependent variable.

Deaths

The occurrence of the permanent cessation of all vital functions in a living organism, marking the end of life.

Degrees of Freedom

Refers to the number of independent values or quantities that can vary in a statistical analysis without breaking any constraints.