MATH 106A - CALCULUS II
WINTER 2007
QUIZ 3
NAME:
Show ALL your work CAREFULLY.
(a) Consider the initial value problem
dy
dx =x−y
with y(1) = 2.
Estimate the value y(2) (when x= 2) of the solution using Euler’s method with
two steps with initial point (1,2). DO THIS BY HAND and show all your steps.
(b) Find the exact area of the region bounded by the curve y=x3+ 1, the line
y= 2, and the y-axis.
(c) Set up (but DO NOT evaluate) a definite integral representing the exact
volume of the solid obtained by rotating the region in (b) around the x-axis.
Date: January 29, 2007.
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