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Evaluate - Calculus - Exam, Exams of Calculus

National Institute of Industrial EngineeringCalculus

Key points of this past exam of Calculus are: Evaluate or Simplify, Values, Function, Estimate, Integral is Improper, Determine, Converges, Differential Equation, Solution, Expression Involving Integral

Typology: Exams

2012/2013

Uploaded on 03/16/2013

gannak
gannak 🇮🇳

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NAME:
Math 106 - Exam 1 - February 1, 2008
Instructions: Show all of your work and circle your final answers. Your work should flow logically and
be easy to follow. Cross out any work that you do not want considered. Calculators are allowed, but notes
and books are not.
Problem Max Score
1 18
2 10
3 16
4 6
5 10
6 10
TOTAL 70
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pf4
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NAME:

Math 106 - Exam 1 - February 1, 2008

Instructions: Show all of your work and circle your final answers. Your work should flow logically and be easy to follow. Cross out any work that you do not want considered. Calculators are allowed, but notes and books are not.

Problem Max Score

TOTAL 70

  1. (18 points) Evaluate the following:

(a)

∫ (^) e

1

cos (ln x) x

dx.

(b)

x

2 x − 1 dx.

  1. (16 points) Consider the IVP y′^ =

y^2 1 + t^2

, y(0) = 1.

(a) By hand, use Euler’s method with step size ∆t = 1 to approximate y(2).

(b) Using the technique of separation of variables, find the solution to the above IVP.

  1. (6 points) Write down an integral that gives the length of the curve y =

x from x = 1 to x = 4.

  1. (10 points) Consider the region in the xy-plane bounded by the graphs of x = y^2 − 4 and y = −x + 2. Find an integral (or sum of integrals) that represents the area of the region. You do not need to evaluate the integral(s).