Evaluate $\iint _ { S } f ( x , y , z ) d S$

question 29

Multiple Choice

Evaluate $\iint _ { S } f ( x , y , z ) d S$ . $f ( x , y , z ) = 5 x + 6 y + z$ ; S is the part of the cone $z = \sqrt { x ^ { 2 } + y ^ { 2 } }$ between the planes $z = 1$ and $z = 4$ .

• A) \(126 \pi \sqrt { 2 }\)
• B) \(42\) \(\pi \sqrt { 2 }\)
• C) \(126 \sqrt { 2 }\)
• D) 0

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Definitions:

Future Value

The worth of a current asset on a future date, calculated by estimating its growth rate over a specific period.

Compound Interest

Interest on both the initial principal and the accumulated interest from previous periods on a deposit or loan.

Future Value

The worth of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today.

Compounded Quarterly

Referring to interest that is calculated and added to the principal amount at the end of each quarter, leading to exponential growth.