Piecewise Continuous - Calculus - Exam, Exams of Calculus

This is the Exam of Calculus which includes Concern Derivatives, Unit Vectors, Approximate the Number, Transformation etc. Key important points are: Piecewise Continuous, Function, Graphed Below, Left Endpoint, Riemann Sum, Approximation, Represents Graphically, Actual Value, Absolute Maximum, Achieve

Typology: Exams

2012/2013

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Simon Fraser University
Department of Mathematics
Burnaby Campus
MATH 152-3, Calculus II
Spring 2006 – Midterm 1
February 8th, 2006, 8:30 – 9:20
Last Name (please print): _________________________________________
First Name (please print): _________________________________________
SFU email ID: _________________________________________
Instructor: P. Menz
Instructions:
1. DO NOT OPEN THIS BOOKLET UNTIL
TOLD TO DO SO.
2. Fill in the above box.
3. This exam contains 7 pages with a total of
6 questions. Once the exam begins please
check to make sure your exam is
complete.
4. SHOW ALL YOUR WORK!
5. If you run out of space in a problem, use
the space on the back of the previous page
and clearly indicate where the solution
continues.
6. Only scientific, non-programmable
calculators with no differentiation and
integration capabilities are allowed.
7. No book, paper, or device, other than the
usual writing instruments, this booklet and
an acceptable calculator, shall be within
reach of a student during the examination.
8. During the examination, speaking to,
communicating with, or deliberately
exposing written papers to the view of
other examinees is forbidden.
Do not write in this table!
Question Marks
1 /8
2 /4
3 /7
4 /6
5 /5
Total /30
pf3
pf4
pf5

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Simon Fraser University Department of Mathematics Burnaby Campus

MATH 152 -3, Calculus II Spring 2006 – Midterm 1 February 8th, 2006, 8:30 – 9:

Last Name (please print): _________________________________________

First Name (please print): _________________________________________

SFU email ID: _________________________________________

Instructor: P. Menz

Instructions:

  1. DO NOT OPEN THIS BOOKLET UNTIL TOLD TO DO SO.
  2. Fill in the above box.
  3. This exam contains 7 pages with a total of 6 questions. Once the exam begins please check to make sure your exam is complete. 4. SHOW ALL YOUR WORK!
  4. If you run out of space in a problem, use the space on the back of the previous page and clearly indicate where the solution continues.
  5. Only scientific, non-programmable calculators with no differentiation and integration capabilities are allowed.
  6. No book, paper, or device, other than the usual writing instruments, this booklet and an acceptable calculator, shall be within reach of a student during the examination.
  7. During the examination, speaking to, communicating with, or deliberately exposing written papers to the view of other examinees is forbidden.

Do not write in this table!

Question Marks

(^1) /

2 /

3 /

4 /

5 /

Total /

  1. Let f ( ) x be the piecewise continuous function graphed below and

.

4 0

I = ∫ f ( ) x dx

a) Show on the graph above what I represents graphically. [1 mark] b) Compute L 4 , the left-endpoint Riemann sum approximation of I , and show on the graph to the right what L 4 represents graphically. [3 mark]

c) Compute , the left-endpoint Riemann sum approximation of I , and show on the graph to the right what represents graphically. [3 mark]

R 4

R 4

d) Which of the approximations L 4 and is closer to the actual value of I? [1 mark]

R 4

  1. Consider the curves y =cos x ,

π

y = x − and x = 0 in the first quadrant.

a) Sketch the curves and shade the area they bound. [2 marks]

b) Set up an integral to find the area. [2 marks]

c) Compute the integral. [3 marks]

  1. Consider the region below. Set up but do not compute an integral for the volume obtained by rotating the region below about the line. Do not simplify the integral. [6 marks]

y = − 1