Use Part 1 of the Fundamental Theorem of Calculus to Find

question 51

Multiple Choice

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.
$$h ( x ) = \int _ { 1 } ^ { \sqrt { x } } \frac { 5 z ^ { 2 } } { z ^ { 4 } + 1 } d z$$
Select the correct answer.

• A) \(\frac { 5 \sqrt { x } } { x ^ { 2 } + 1 }\)
• B) \(\frac { \sqrt { x ^ { 2 } + 1 } } { 5 }\)
• C)\(\frac { 5 \sqrt { x } } { 2 \left( x ^ { 2 } + 1 \right) }\)
• D) \(\frac { \sqrt { x + 5 } } { x ^ { 2 } + 5 }\)
• E) none of these

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Definitions:

Income Effect

The impact on consumer's choice arising from a change in their income, influencing their purchasing power.

Giffen Good

A type of inferior good for which demand increases as the price increases, violating the basic law of demand.

Inferior Good

A type of good whose demand decreases when consumer income rises, and vice versa, often contrasted with normal goods whose demand increases with rising income.

Normal Good

A good for which demand increases when consumer income rises, and decreases when consumer income falls.