Find the Formula and Limit as Requested $f ( x ) = 6 x ^ { 2 } + 2$

question 76

Multiple Choice

Find the formula and limit as requested.
-For the function $f ( x ) = 6 x ^ { 2 } + 2$ , 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) \(6 + \frac { 324 n ^ { 3 } + 486 n ^ { 2 } + 162 n } { 6 n ^ { 3 } } ;\) Area \(= 60\)
• B) \(6 + \frac { 324 n ^ { 3 } + 486 n ^ { 2 } + 162 n } { 6 n ^ { 3 } } ;\) Area \(= 54\)
• C) \(6 + \frac { 324 n ^ { 3 } + 486 n ^ { 2 } + 162 n } { 6 n ^ { 4 } } ;\) Area \(= 6\)
• D) \(6 + \frac { 324 n ^ { 3 } + 486 n ^ { 2 } + 162 n } { 6 n ^ { 4 } } ;\) Area \(= 60\)

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Definitions:

Main Connective

In logic, the operator within a proposition that determines the proposition's overall truth value; it links the main components of the proposition.

Symbolize

To represent or stand for something else, especially through the use of symbols or imagery.

Negation

A compound statement whose truth value is the opposite truth value of its component statement.

Disjunction

A logical operation that results in true if at least one of its premises is true.