Find the Formula and Limit as Requested $f ( x ) = 12 - 2 x ^ { 2 }$

question 35

Multiple Choice

Find the formula and limit as requested.
-For the function $f ( x ) = 12 - 2 x ^ { 2 }$ , find a formula for the lower sum obtained by dividing the interval $[ 0,1 ]$ into $n$ equal subintervals. Then take the limit as $n \rightarrow \infty$ to calculate the area under the curve over $[ 0,1 ]$ .

• A) \(12 - \frac { 4 n ^ { 3 } + 6 n ^ { 2 } + 2 n } { 3 n ^ { 3 } }\); Area \(= \frac { 34 } { 3 }\)
• B) \(\frac { 2 n ^ { 3 } + 3 n ^ { 2 } + n } { 3 n ^ { 3 } } ;\) Area \(= \frac { 2 } { 3 }\)
• C) \(12 - \frac { 2 n ^ { 3 } + 3 n ^ { 2 } + n } { 3 n ^ { 3 } } ;\) Area \(= \frac { 34 } { 3 }\)
• D) \(12 + \frac { 2 n ^ { 3 } + 3 n ^ { 2 } + 1 } { 3 n ^ { 3 } } ;\) Area \(= \frac { 38 } { 3 }\)

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Gordon Allport, a psychologist known for his contributions to personality psychology and his theory on the nature of prejudice.