Use the Definition to Find the Taylor Series Centered At c

question 26

Multiple Choice

Use the definition to find the Taylor series centered at
$c = 0 \text { for the function }$ $f ( x ) = 3 \ln \left( x ^ { 2 } + 1 \right)$

• A)\(3 \ln \left( x ^ { 2 } + 1 \right) = \sum _ { n = 0 } ^ { \infty } \frac { ( 3 x ) ^ { 2 n + 2 } } { n + 1 }\)
• B)\(3 \ln \left( x ^ { 2 } + 1 \right) = 3 \sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \frac { x ^ { n + 1 } } { n + 1 }\)
• C)\(3 \ln \left( x ^ { 2 } + 1 \right) = 3 \sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \frac { x ^ { 2 n + 2 } } { n + 1 }\)
• D)\(3 \ln \left( x ^ { 2 } + 1 \right) = 3 \sum _ { n = 0 } ^ { \infty } \frac { x ^ { 2 n + 2 } } { n }\)
• E)\(3 \ln \left( x ^ { 2 } + 1 \right) = \sum _ { n = 0 } ^ { \infty } \frac { ( 3 x ) ^ { n + 1 } } { n + 1 }\)

Comprehend the functions of cytokinins in plant morphology such as in stem and root swelling.

Recognize the impact of ethylene in plant processes like fruit ripening, leaf abscission, and senescence.

Describe the physiological effects of gibberellins on plant development including seed germination and stem elongation.

Explain how environmental factors and external applications of hormones can influence plant growth and development.

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Definitions:

Test-retest Reliability

The consistency of a test's results when the same subjects take the same test again after a period of time.

Standard Score

A score that has been transformed to fit a normal distribution, usually with a mean of 100 and a standard deviation of 15.

National Mean

The average score or value derived from a specific set of data collected across a nation.

Standard Deviation

The statistical metric that calculates the dispersion or spread of data points in a dataset around the average value.