Review Practice problems

Solve for x in the integration below If X= 5

Multiple choice

If the displacement of a particle on a line is given by Then the number of times the particle changes direction is

Of the following, which has the least value?

Write the set up for finding area under the curve using the limit process from the interval [3,7].

Given that State the interval where

2 -1 1

Approximate using trapezoid rules with 4 subintervals

Solve for x in the integration below If

The acceleration of a particle moving along a straight line is given by a =6t. If,when t =0 its velocity v =1 and its distances =3, then at anytime t the position function is given by

If f is continuous, strictly increasing function on the interval [a, b] as shown below, which of the following must be true?

Given Find f(x)

Free response questions Using a calculator Is recommended

Traffic flow is defined as the rate at which cars pass through an intersection, measured in cars per minute. The traffic flow at a particular intersection is modeled by the function F defined by where F(t ) is measured in cars per minute and t is measured in minutes. (a) To the nearest whole number, how many cars pass through the intersection over the 30-minute period?

Traffic flow is defined as the rate at which cars pass through an intersection, measured in cars per minute. The traffic flow at a particular intersection is modeled by the function F defined by where F(t ) is measured in cars per minute and t is measured in minutes. (b) Is the traffic flow increasing or decreasing at t = 7 ? Give a reason for your answer.

Traffic flow is defined as the rate at which cars pass through an intersection, measured in cars per minute. The traffic flow at a particular intersection is modeled by the function F defined by where F(t ) is measured in cars per minute and t is measured in minutes. (c) What is the average value of the traffic flow over the time interval 10 ≤ t ≤ 15 ? Indicate units of measure.

Traffic flow is defined as the rate at which cars pass through an intersection, measured in cars per minute. The traffic flow at a particular intersection is modeled by the function F defined by where F(t ) is measured in cars per minute and t is measured in minutes. (d) What is the average rate of change of the traffic flow over the time interval 10 ≤ t ≤ 15 ? Indicate units of measure.

Approximate with a Riemann sum, using the midpoints of 5 subintervals of equal length. Using correct units, explain the meaning of this integral.

A particle moves along the y axis with velocity given by a) In which direction (up or down) is the particle moving at time t = 1.5 ? Why?

A particle moves along the y axis with velocity given by b) Find the acceleration of the particle at time t = 1.5. Is the velocity of the particle increasing at t = 1.5? Why or why not?

A particle moves along the y axis with velocity given by c) Given that y(t) is the position of the particle at time t and that y(0) = 3. Find y(2).

A particle moves along the y axis with velocity given by d) Find the total distance traveled by the particle from t = 0 to t = 2.

A metal wire of length 8 centimeters (cm) is heated at one end A metal wire of length 8 centimeters (cm) is heated at one end. The table above gives selected values of the temperature T ( x), in degrees Celsius (°C), of the wire x cm from the heated end. The function T is decreasing and twice differentiable. Estimate the average temperature of the wire using a trapezoidal sum with the four (uneven) subintervals indicated by the data in the table. Indicate units of measure.

ANS