DQ 1

Question 1

For this question, treat 'y' as an independent variable.

$$\frac{d}{dy} \left( ln(y) \right) = ? \nonumber$$

A.

$$\frac{1}{y} \nonumber$$

B.

$$\frac{2}{y} \nonumber$$

C.

$$\frac{1}{2} y^2 + 3 \nonumber$$

D.

$$4x \nonumber$$

E.

$$none of the above \nonumber$$

Question 2

For this question, treat 'y' as an independent variable.

$$\frac{dy}{y} = ? \nonumber$$

A.

$$\frac{2}{x} \nonumber$$

B.

$$d \left( ln(y) \right) \nonumber$$

C.

$$\frac{1}{2} e^{3y} \nonumber$$

D.

$$ln(x) \nonumber$$

E.

$$none of the above \nonumber$$

Question 3

For this question, treat 'V' as in independent variable.

$$\int_{V_1}^{V_2} \frac{1}{V} dV = ? \nonumber$$

A.

$$ln(V_2) - ln(V_1) \nonumber$$

B.

$$ln ( V_2 - V_1) \nonumber$$

C.

$$ln \left ( \frac{V_2}{V_1} \right) \nonumber$$

D.

$$ln(Y) \nonumber$$

E.

$$none of the above \nonumber$$

Question 4

For this question, treat 'V' as in independent variable.

$$\int_{V_1}^{V_2} \frac{dV}{V} = ? \nonumber$$

A.

$$ln(V_2) - ln(V_1) \nonumber$$

B.

$$ln ( V_2 - V_1) \nonumber$$

C.

$$ln \left ( \frac{V_2}{V_1} \right) \nonumber$$

D.

$$ln(Y) \nonumber$$

E.

$$none of the above \nonumber$$

Question 5

For this question, treat 'V' as in independent variable.

$$\int_{V_1}^{V_2} d(ln(V)) = ? \nonumber$$

A.

$$ln(V_2) - ln(V_1) \nonumber$$

B.

$$ln ( V_2 - V_1) \nonumber$$

C.

$$ln \left ( \frac{V_2}{V_1} \right) \nonumber$$

D.

$$ln(Y) \nonumber$$

E.

$$none of the above \nonumber$$