Review for Third and Fourth parts (section 008)
Note from the instructor: I have put together the review exams for the third and fourth parts of the course, as we commented in class. Both tests were very good, although the fourth had many repeated questions, and some questions that did not belong in this part. I have changed the coefficients of all problems to prevent the use of answer keys.
- Compute the following indefinite integrals:
- Using the Fundamental Theorem of Calculus, evaluate the following definite integrals:
- Find the area under the curve between and
- Compute the net area of the function between and
- Find an antiderivative of that satisfies
- A vintage toy was worth $33 in 1970 and its price increased at a rate of 19% per year.
- Find an equation of the value of the toy in dollars, years after 1970.
- Find the average cost of the toy over the period from 1970 to the year 2013.
- What year was the closest to the average cost of the toy?
- If the demand and supply are given by and :
- Which one is the demand, and which one is the supply?
- Find consumer and producer surplus at equilibrium
- Find the area of the region bounded by the graphs of and
- Find the area of the region bounded by the graphs of and from to
- (Note from the instructor: this problem is awesome. Challenging, but really good to test many of your algebraic skills) The yearly consumption of fruit in the US increased exponentially since 1900 at a continuous rate of 2.9% per year. The amount of fruit consumed in 1950 was 4.5 million pounds.
- Find a formula for the yearly consumption of fruit in millions of pounds, as a function of time in years since 1900.
- Find the average yearly fruit consumption between 1950 and the year 2000.
- During what year was fruit consumption closest to average?
- The mall cops at Five Finger Discount Mall noticed an increase in department store theft after their local economy plummeted. In one particular store, they recorded the dollar amount of all items stolen from 2000 to 2010. The yearly amount of stolen items is listed below:
Estimate the average dollar amount of items stolen from 2005 to 2010.
- If is measured in days since June 1st, the inventory for an item in a warehouse is given by Find the average inventory in the warehouse during the 60 days after June 1st.