This preview shows page 1. Sign up to view the full content.
Math 262
/
Fall 2008
Dec. 17, 9:00am

12:00pm
Problem 1 (10 marks). Find the interval of convergence,
including
the end points,
of the foliowing
power
series:
,.,,,
Efr{,,)"
*
^3n
rn \'
\"./
,/
t,
4^
+tL
1
Problem 2 (10 marks). Consider
the function
/(r)
Use a series
to
approximate
the value of
/(0.t)
with error at most 105.
S,/Problem
3 (10 marks). Find the recunence
relation for the solutions
to the dif
ferential equation
(7

,)'u" *'y
=
0 abor.rt
the origin. Give the first three
l:tolrzero
terrns of two linearly
independent
solutioris
to tlie equaiotr'
Lr/
probnem
4 (10 marks). Cornplete
both of the foliowing problenrs:
(a) Find
the
length
of
the curve
r(t)
:6t
i +3*
j+t3
k from
f
:0
to t:I.
(b) Compute
the curvature
function n.(t)
for the curve
r(t)
: (t
+ cost)i +
(t

cost)j + r4sint
k,
'
Problem 5 (10 marks). Consider
the following pair of equations:
tu*Yu*Y2nu
:
3
'u2
+'u'
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 10/16/2010 for the course MATH 262 taught by Professor Faber during the Winter '08 term at McGill.
 Winter '08
 FABER
 Calculus

Click to edit the document details