Solve the Problem $\tan ^ { - 1 } x$ , Obtain a Series For

question 361

Multiple Choice

Solve the problem.
-Using the Maclaurin series for $\tan ^ { - 1 } x$ , obtain a series for $\frac { \tan ^ { - 1 } x ^ { 2 } } { x ^ { 2 } }$ .

• A) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } x ^ { 4 n } } { 2 n + 2 }\)
• B) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } x ^ { 2 n } } { 2 n + 1 }\)
• C) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } x ^ { 2 n } } { 2 n + 2 }\)
• D) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } x ^ { 4 n } } { 2 n + 1 }\)

Understand the effects of sample size and confidence levels on the margin of error and confidence intervals for population means and proportions.

Grasp the concept of level of significance (α) and its relation to confidence levels.

Comprehend how sample size influences the degrees of freedom in a t-distribution.

Distinguish the factors that affect the margin of error in confidence intervals and the computation of sample sizes for such intervals.

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