Find the Formula and Limit as Requested $\mathrm { f } ( \mathrm { x } ) = 4 \mathrm { x } + 3$

question 22

Multiple Choice

Find the formula and limit as requested.
-For the function $\mathrm { f } ( \mathrm { x } ) = 4 \mathrm { x } + 3$ , find a formula for the upper sum obtained by dividing the interval [0,3] into $n$ equal subintervals. Then take the limit as $n \rightarrow \infty$ to calculate the area under the curve over $[ 0,3 ]$ .

• A) \(9 + \frac { 33 n ^ { 2 } + 37 n } { 2 n ^ { 2 } } ;\) Area \(= \frac { 51 } { 2 }\)
• B) \(9 + \frac { 36 n ^ { 2 } + 36 n } { 2 n ^ { 2 } } ;\) Area \(= \frac { 54 } { 5 }\)
• C) \(9 + \frac { 36 n ^ { 2 } + 36 n } { 2 n ^ { 2 } } ;\) Area \(= 27\)
• D) \(9 - \frac { 36 n ^ { 2 } + 36 n } { 2 n ^ { 2 } } ;\) Area \(= - 9\)

Identifying strategies to overcome challenges in decision-making and problem-solving.

Differentiating between various decision-making approaches and their applications.

Analyzing the role of technology and information in enhancing decision-making.

Acknowledging the significance of collaborative decision-making and the principles guiding it.

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Definitions:

Descriptive Statistics

Statistics that summarize, describe, and analyze a set of data, providing insights into its central tendency, variability, and distribution.

Assumption of Normality

The presumption that the data in a dataset is normally distributed, which is a common precondition for many statistical tests.

Descriptive Statistics

Statistical methods that describe and summarize data through measures such as mean, median, mode, and standard deviation.

Variables

Variables are symbols or names that represent values or characteristics that can vary within a study or experiment.