Use the Definition to Find the Taylor Series Centered At c

question 25

Multiple Choice

Use the definition to find the Taylor series centered at $c = \frac { \pi } { 4 } \text { for the function }$ $f ( x ) = \cos x$

• A)
• \[\cos x = \frac { \sqrt { 2 } } { 2 } \sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { \frac { n ( n - 1 ) } { 2 } } \left( x + \frac { \pi } { 4 } \right) ^ { n } } { n ! }\]
• B)
• \[\cos x = \frac { \sqrt { 2 } } { 2 } \sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { \frac { n ( n + 1 ) } { 2 } } \left( x - \frac { \pi } { 4 } \right) ^ { n } } { n ! }\]
• C)
• \[\cos x = \sqrt { 2 } \sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } \left( x - \frac { \pi } { 4 } \right) ^ { n } } { n ! }\]
• D)
• \[\cos x = \sqrt { 2 } \sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { \frac { n ( n - 1 ) } { 2 } } \left( x + \frac { \pi } { 4 } \right) ^ { n } } { n ! }\]
• E)
• \[\cos x = \frac { \sqrt { 2 } } { 2 } \sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } \left( x - \frac { \pi } { 4 } \right) ^ { n } } { n ! }\]

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Definitions:

Familywise Error

The overall likelihood that a Type I error (incorrect rejection of a true null hypothesis) will occur across a set of related hypotheses.

Type I Error

Error that occurs when the null hypothesis is true but the decision is made to reject the null hypothesis.

Probability

Likelihood of occurrence of a particular outcome of an event given all possible outcomes.

Familywise Error

The probability of making one or more false discoveries, or type I errors, when performing multiple hypotheses tests.