Math 116 Practice Midterm 3

Printable Key

Problem 1

Integrate the following.  If the integral is improper and diverges, state this.  If the integral is improper and converges evaluate it.

A. 

Solution

B. 

Solution

C. 

Solution

D. 

Solution

Problem 2

The population P (in billions) of the world at time t years after 2,000 can be modeled by the equation

If in the year 2000, there were 6 billion people in the world.  What will the population be in the year 2040?

Solution

Problem 3

Consider the integral

A.  Use the Trapezoidal Rule to approximate this integral with n  =  4.

Solution

B.  Use Simpson's Rule to approximate this integral with n  =  4.

Solution

C.  Use the fact that |2cos(x²) - 4x²sin(x²)| < 3 to find a bound on the error from part A.

Solution

Problem 4

Consider the function

        y  =  4sin(2x)

A.  Find the radian measure for the angle 15^o.

Solution

B. Without the use of a calculator determine the period an amplitude of the graph.  Use this information to sketch the graph. 

Solution 

C.  Use part A. to determine the equation of the tangent line to the graph at the angle 15^o.  Then sketch this line on the graph.