Exam 4 Review - Survey of Calculus | MATH 1241, Exams of Calculus

Material Type: Exam; Class: Survey of Calculus; Subject: Mathematics; University: Clayton State University; Term: Unknown 1989;

Typology: Exams

Pre 2010

Uploaded on 08/04/2009

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MATH 1241 - Spring 20xx- Test 4 NAME: _________________________
Sections 4.5, 5.2, 5.3, 6.1, 6.2, 6.5, 6.6
1. Using your computer, approximate the area of the region between the graph of the
function
xxxf 2)ln()(
and the x-axis on the interval from x=1.19 to x=3.59
using the right endpoint rule with 12 rectangles.
2. The number of medical school students (in thousands) from 1982 through 1992,
reported each fall semester, can be modeled by
1.7008.24.0021.0)(
23
ttttm
thousand students where t represents the
number of years since 1980.
A) Find any relative (local) maximum or minimum points on the model between 1982
and 1992 using calculus. Justify your answer by describing all steps that you use to
get your answers.
B) Although m(t) is continuous, it must be discretely interpreted because only integer-
valued inputs make sense in the context of this problem. With this restriction in
mind, determine the year in which the number of medical students was greatest and
when it was the least from 1982 to 1992. Give the number of medical students in each
case. [3 points]
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MATH 1241 - Spring 20xx- Test 4 NAME: _________________________ Sections 4.5, 5.2, 5.3, 6.1, 6.2, 6.5, 6.

  1. Using your computer, approximate the area of the region between the graph of the function f^ (^ x )^ ln( x )^2 x and the x- axis on the interval from x =1.19 to x =3. using the right endpoint rule with 12 rectangles.
  2. The number of medical school students (in thousands) from 1982 through 1992, reported each fall semester, can be modeled by m ( t ) 0. 021 t^3  0. 4 t^2  2. 08 t  70. (^1) thousand students where t represents the number of years since 1980. A) Find any relative (local) maximum or minimum points on the model between 1982 and 1992 using calculus. Justify your answer by describing all steps that you use to get your answers. B) Although m ( t ) is continuous, it must be discretely interpreted because only integer- valued inputs make sense in the context of this problem. With this restriction in mind, determine the year in which the number of medical students was greatest and when it was the least from 1982 to 1992. Give the number of medical students in each case. [3 points]
  1. Little Timmy is participating in a neighborhood turtle racing league. The racing turtles are placed at a starting line and given 4 minutes to travel as far as possible. As part of the training regiment for his turtle, Timmy has equipped his pet with a small speedometer. The speed of Timmy’s turtle at time t is depicted in the graph below. 0 1 2 3 4 2 4 6 8 time in minutes speed in feet per minute A) Approximate the distance traveled by Timmy’s turtle during the four-minute journey using 4 intervals. Draw rectangles on the graph above using left endpoints of each sub-interval and show your work below. B) Is your answer in part A) an overestimate or underestimate of the actual total distance traveled by Timmy’s turtle. Justify why you believe this. C) In a complete sentence, describe what will happen to the approximation of the total distance traveled if you were to use more sub-intervals?