Math 125 Test 1 9 points each Sept. 7, 2000

1. Find the equation of the line:

a. with slope 4 and y intercept 3
b. thru (3,2) with slope -2
c. thru (-1,3) and (1,4)
d. Does the parabola described by the function f(x) = - (1 - 4x)2 + 7x² - (4 - 10x² ) open upwards or downwards?
e. What is the y - intercept of the graph of f(x) = - (x - 2)² + 3x + 1?

2. A biologist conducting an experiment starts with a culture of 300 E.coli bacteria. 72 hours later the culture consists of 600,000 bacteria. What is the average increase in the number of E.coli bacteria per hour?

3. Given that T(y) = y² - 3y + 5, compute T(x + Dx).

4. Consider the piecewise continuous function

. Find .

5. The position of a rocket in miles is given by the position function p(t) = 2t² + 5t - 2 , where t is the time in seconds . What is the rocket's average speed over the time interval [3, 6]?

6. Let

Find the value of k so that

Evaluate the limits.

7.

8 a.

b.

9.

10. Consider the function
a. Is f(x) continuous at x = 0 ?
b. Does the limit exist as x approaches 0 ?

11. Give the graphical definition of the derivative of y = f(x) at the point (a, f(a)). You must use a complete sentences to get any credit at all.

Bonus: 10 points each

1. If you are given that if f(x) = e^x, then f ' (x) = e^x, what can you conclude about the limit ?

2. Which (if either) of set of points represents a linear relationship?

a. b.

R	0	10	20	30	40				P	1	2	3
S	8	18	28	38	48				Q	1	4	9

3. The formula which relates Fahrenheit temperature to Celsius temperature is F =(9/5) C + 32.
What is the temperature at which a Fahrenheit thermometer will give the same reading as a Celsius thermometer?
(you gotta show the work to get the credit).

4. Given that , find the value of
(you gotta show the work to get the credit)