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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
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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:
Do not write in this table!
Question Marks
(^1) /
2 /
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Total /
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4 0
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]
d) Which of the approximations L 4 and is closer to the actual value of I? [1 mark]
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]
y = − 1