Use Part 1 of the Fundamental Theorem of Calculus to Find

question 20

Multiple Choice

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. $$h ( x ) = \int _ { 1 } ^ { \sqrt { x } } \frac { z ^ { 2 } } { z ^ { 4 } + 1 } d z$$

• A) \(\frac { \sqrt { x + 1 } } { x ^ { 2 } + 2 }\)
• B) \(\frac { \sqrt { x ^ { 2 } + 1 } } { 2 }\)
• C)
• \(\frac { \sqrt { x } } { 2 \left( x ^ { 2 } + 1 \right) }\)
• D) \(\frac { \sqrt { x } } { x ^ { 2 } + 1 }\)
• E) none of these

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Definitions:

Incremental Income

The additional income generated from undertaking a specific action or investment, compared to not doing so.

Variable Costs

Expenses that change in proportion to the level of production or sales activity, such as raw materials and direct labor costs.

Fixed Costs

Costs that do not change with the level of production or sales activities, such as rent, salaries, and insurance premiums.

Variable Manufacturing Overhead

Costs that vary with production volume, such as utilities and materials, which are only incurred as a result of manufacturing activities.