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Applied Math-Intro Calculus Exam: 8 Problems to Solve | MATH 106, Exams of Advanced Calculus

Material Type: Exam; Class: Applied Math-Intro Calculus; Subject: Mathematics; University: Christian Brothers University; Term: Fall 2006;

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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EXAM 3
Math 106
October 12, 2006
Name
You must show all your work. Partial credit will be given. Each problem is worth 6 points.
1. Find the general antiderivative for each of the functions.
(a) s(t) = t3
3t2+ 3t1.
(b) f(x) = 4x2+ 2t1+ 1.
(c) g(t) = 2t.
(d) y=4x3
15
x2.
pf3
pf4
pf5

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EXAM 3

Math 106 October 12, 2006

Name

You must show all your work. Partial credit will be given. Each problem is worth 6 points.

  1. Find the general antiderivative for each of the functions.

(a) s(t) = t^3 − 3 t^2 + 3t − 1.

(b) f (x) = 4x−^2 + 2t−^1 + 1.

(c) g(t) = 2t.

(d) y = 4 x^3 − 15 x^2

  1. Find all the inflection points for displaystyleg(x) = (^) x (^23) +.
  2. Use the second derivative test to determine all relative maximums and relative minimums for f (x) = −x^4 − 2 x^3 + 12x^2.

(e)

− 1

3 x + 4 dx

(f)

1

(−x^2 + 4x − 3) dt

  1. Based on 1.5 minutes of data the velocity of a certain minivan may be modeled by

V (t) = − 2. 133 t^3 + 3. 999 t^2 − 0. 1533 t + 0. 3167

miles per minute, where t is the number of minutes since measurement began. Find a position function D(t) which describes the distance traveled by the minivan since measurement began.

  1. Use a left hand sum with n = 10 to estimate the area between the graph of y = x^2 − 2 x^ and the x axis on the interval [2, 4].
  2. Use a right hand sum with n = 5 to estimate the area between the graph of s(t) = ln (t) and the horizontal axis on the interval [1, e].
  3. Find the exact area between the graph of y = ex^ − x^2 and the x-axis from x = 0 to x = 2.