CLEP Calculus Practice Test

The key concept is the constant rate of water flow, and since the tank is being filled at 10 cubic meters per hour, after 3 hours it will contain 10 * 3 = 30 cubic meters of water. This calculation is based on the principle of constant rates of change, where the amount of water added is directly proportional to the time elapsed.

The key concept is the relationship between the area and radius of a circle, given by the formula A = π$r^{2}$. The correct option is "2 centimeters" because the rate of change of the area is dA/dt = 2πr(dr/dt), and given dA/dt = 4π and dr/dt = 1, solving for r yields r = 2.

Distance traveled is calculated by multiplying velocity by time, so the car travels 60 miles per hour * 2 hours = 120 miles. This demonstrates the key concept of distance as the product of velocity and time.

The key concept is the relationship between rate and accumulation over time, where the amount of water accumulated is the product of the fill rate and the duration. The tank is being filled at 2 cubic meters per minute, so after 5 minutes, it will contain 2 * 5 = 10 cubic meters of water.

3 is correct because the average value is (1/(b-a)) * integral of f(x) from a to b, which equals (1/(3-1)) * integral of 3 from 1 to 3, and this equals (1/2) * [3x] from 1 to 3, which equals (1/2) * 3 * (3 - 1) = (1/2) * 3 * 2 = 3.

3 is correct because the average value is (1/(b-a)) * integral of f(x) from a to b, which equals (1/(4-2)) * integral of x from 2 to 4, and this equals (1/2) * [$x^{2}$/2] from 2 to 4, which equals (1/2) * (1/2) * ($4^{2}$ - $2^{2}$) = (1/4) * (16 - 4) = (1/4) * 12 = 3.

-5 is correct because by the Fundamental Theorem of Calculus, the integral from a to x is the negative of the integral from x to a, since the limits are reversed.

The key concept is applying the power rule of integration, which states that ∫$x^{n}$ dx = ($x^{n+1}$)/(n+1). Integrating 2x+1 from 2 to 4 yields [($x^{2}$)+x] from 2 to 4, which equals [($4^{2}$)+4] - [($2^{2}$)+2], resulting in 14.

The limit of a Riemann sum as the number of subintervals approaches infinity is correct because by definition, the definite integral is the limit of a Riemann sum as the number of subintervals increases without bound.

0.0693 is correct because y' = ky implies y(t) = y(0)$e^{kt}$, so 2y(0) = y(0)$e^{10k}$, and solving for k gives k = ln(2)/10 = 0.0693.