007B Sample Midterm 1

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This is a sample, and is meant to represent the material usually covered in Math 7B for the midterm. An actual test may or may not be similar.

Click on the  boxed problem numbers  to go to a solution.

 Problem 1 

Let  .

(a) Compute the left-hand Riemann sum approximation of    with    boxes.

(b) Compute the right-hand Riemann sum approximation of    with    boxes.

(c) Express    as a limit of right-hand Riemann sums (as in the definition of the definite integral). Do not evaluate the limit.

 Problem 2 

A population grows at a rate

where    is the population after    months.

(a)   Find a formula for the population size after    months, given that the population is    at  

(b)   Use your answer to part (a) to find the size of the population after one month.

 Problem 3 

Evaluate the following integrals.



 Problem 4 

Evaluate the following integrals.



 Problem 5 

Find the area bounded by    and    from    to  

Contributions to this page were made by Kayla Murray