Time and Date Stamps (logged): 17:12:20 06-10-2020 °¶Ÿ°±Ÿ±¯¯µŸ°¯Ÿ±¯±¯ Precalculus II

Calculus I Test 1


Completely document your work and your reasoning.

You will be graded on your documentation, your reasoning, and the correctness of your conclusions.


Test should be printed using Internet Explorer.  If printed from different browser check to be sure test items have not been cut off.  If items are cut off then print in Landscape Mode (choose File, Print, click on Properties and check the box next to Landscape, etc.). 

Name and Signature of Student _____________________________

Signed by Attendant, with Current Date and Time: ______________________

If picture ID has been matched with student and name as given above, Attendant please sign here:  _________

Instructions:

Directions for Student:

Test Problems:

.    .    .    .    .     .    .    .    .     .    .    .    .     .    .    .   

.

.

.

.

.

.

.

.

.

.

Problem Number 1

Sketch the graph of f(x) = 1 / (x + 6), from x = -4 to x = 5, then use this graph to sketch the graph of the derivative function f ' (x) over the same interval.

.

.

.

.

.

.

.

.

.

.

Problem Number 2

The cost in dollars of producing n steel bars is C(n).

.

.

.

.

.

.

.

.

.

.

Problem Number 3

Explain in terms of rates and amounts why and how, given the values of a derivative function y ' (t) at two nearby t values, we can estimate the change in its antiderivative y(t) between these t values by averaging two values of y ' (t) and multiplying by the corresponding time interval.

.

.

.

.

.

.

.

.

.

.

Problem Number 4

The rate at which dollars flow into your bank account is rate = 4 * 2^( .12 t), where rate is in dollars per day when t is time in months from an initial investment.   Use two 2-interval approximations to estimate the change in the value of your account between t = 9 months and t = 15 months.  One of your approximations should be an overestimate, the other an underestimate.

 

.

.

.

.

.

.

.

.

.

.

Problem Number 5

In terms of two simple examples involving money, pay rate and time, explain the difference between a situation where you obtain a meaningful result by subtracting two quantities and dividing by a time interval and a situation where you obtain a meaningful result by averaging two quantities and multiplying by a time interval. Be sure to explain your results in terms of units and also in terms of meanings.

In terms of two simple examples involving velocity, distance and time, explain the difference between the meaning of the slope of a trapezoid and the area of a trapezoid. Be sure to explain your results in terms of units and also in terms of meanings.

.

.

.

.

.

.

.

.

.

.

Problem Number 6

Solve using ratios instead of functional proportionalities: 

.

.

.

.

.

.

.

.

.

.

Problem Number 7

Problem: The quadratic depth vs. clock time model corresponding to depths of 24.06623 cm, 10.40932 cm and 3.029289 cm at clock times t =  10.98677, 21.97353 and 32.9603 seconds is depth(t) = .026 t2 + -2.1 t + 44.

Problem: The depth function depth(t) = .026 t2 + -2.1 t + 44 corresponds to depths of 24.06623 cm, 10.40932 cm and 3.029289 cm at clock times t = 10.98677, 21.97353 and 32.9603 seconds.