Math

hw4.docx

1. Let (x) = 3^x . Tabulate the change of over the intervals (i) 1,3] , (ii) 1,2] , (iii) 1,-1] , (iv) 1,1.2] , (v) 1,1.1] , (vi) 1,1.01] . Graph = 3^x together with the secant line passing through 1,f(1)) and 1.1, f(1.1)) .

ttp://calculus.sfsu.edu/latexrender/pictures/5d62e1d04bde9c56bce2f73be50b611b.png

Based on the pattern of numbers (without deriving a general formula), estimate how quickly (x) = 3^x changes at = 1 .

2. Let (x) = e^x where = 2.71 . Tabulate the change of over the intervals(i) 0,2] , (ii) 0,1] , (iii) 0,.5] , (iv) 0,0.25] , (v) 0,0.1] .

ttp://calculus.sfsu.edu/latexrender/pictures/2c5902ba35fb322e22af98d09f0fb77a.png

Estimate the rate of change of (x) = e^x at = 0 . Check your answer with this video:

http://www.youtube.com/watch?feature=player_embedded&v=6B0UUVdtDms

3. Cyclists A and B rode along a straight one way road starting from the same location and they rode for one hour. Cyclist A rode half the time with speed 10 mileshour and the other half time with speed 30 mileshour. Cyclist B rode half the total distance with speed 10 mileshour and half the distance with speed 30hours.

(a) Calculate the total distance traveled by cyclist A. Graph the velocity function for cyclist A and calculate the average trip velocity for cyclist A.

(b) Calculate the total distance traveled by cyclist B. Calculate the average velocity for cyclist B. Graph the velocity function for cyclist B.

4. Use the limit definition of the rate of change to calculate how quickly (x) = x^2 changes at =-4 .

5. Go to a financial website (for exmaple, finance.google.com), pick your favorite stock. By (t) denote the price at which the stock was exchanged at time where is measured in seconds from last Friday midday. What does (0) mean? What does (7200) mean? Estimate the average rate of change of the stock for the following time intervals

ttp://calculus.sfsu.edu/latexrender/pictures/d09f930d617ff0cf41d53f56aee9e704.png

Based on your calculations do you think the instantaneous rate of change of the price (t) exist? Can you briefly describe in words the behavior of (t) near = 0 .

6. youtube.com/watch?v=zrpjns9rk3Y Join Professor Goetz on his glider flight from Pedra Bonita, Rio, Brazil to the beach. While watching it try to match these graphs obtained by the GPS. Then answer the following questions:

(a) What was the total descent of the flight? How long did it last?

(b) What was the average rate of descent throughout the flight? (What are the units?)

(d) Was there a time interval when the glider was ascending?

7. If a house bought for \$1000000 appreciates at an annual percentage rate of 20%, what is the average dollar rate of change of its price during (a) the first year, (b) the second year, (c) the third year? What are the units of these rates of change?

8. (a) The Standard & Poor's/Case-Shiller 20-city housing index fell 16.3% in July 2008 from a year earlier.

(b) Home prices were tumbling by the sharpest annual rate ever in July 2008.

(c) However, the rate of monthly declines was slowing in July 2008.

Denote (t) - the value of the index at time , _(annual)(t) - annual rate of (t) and _(monthly)(t) - monthly rate of (t) . Write down the formulas for and terms of (t) . Explain and interpret (a), (b), (c).