Plz do it and give it to me ASAP
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MAT2280_Test04_Spr18.docMAT 2280 Test 04 Spring 2018
Each problem is worth 8 points unless otherwise indicated. You must show all your work on paper to receive credits. Answers alone will receive no credits.
For problems 1 through 4, find a Maclaurin series for the function and determine radius of convergence
1)
1
()
8
fx
x
=
+
2)
2
()
x
fxxe
-
=
3)
()sin3
fxxx
=
4)
()ln(3)
fxex
=+
5) Find the radius of convergence and interval of convergence of the following series:
(
)
(
)
1
1
13
3
nn
n
n
x
n
+
¥
=
--
å
6) Find the Taylor series for sinx centered at a =
4
p
(Use sigma notation for the final series whenever possible)
7) Use power series of sinhx to find the following indefinite integral
sinh
x
dx
x
ò
8) Two forces
12
FandF
with magnitude 10 lb and 12 lb exerted at a point P at the origin
1
F
makes an angle of0
30
with the positive x-axis , and2
F
makes an angle of0
45
with the negative x-axis.a) Find the components of
12
FandF
b) Find the magnitude and direction of resultant force
F
of12
FandF
9)
(1,2,4)
LetV
=--
r
. Find the direction angles,,
abg
ofV
r
10) (12 points)
(2,3)(4,5)
)
)23
)
)
LetUandV
aFindUV
bFindUV
cFindUV
dFindUV
=-=-
+
-
-
·
rr
rr
rr
rr
rr
11) (12 points)
(2,3,1)(4,5,2),(1,2,0)
)
)
)()
)Pr
V
LetUandVandW
aFindUV
bFindUV
cFindWUV
dFindojU
=-=-=-
´
´
·´
r
uur
rr
rr
rr
uur
rr
r
Formulas you can use:
(
)
(
)
(
)
()
0
00
(21)
1
10
2(21)
00
2
0
()
()()
!
1
1!
ln(1)1sin1
(21)!
cos1sinh
2!(21)!
cosh
2!
n
n
n
n
nx
nn
nn
nn
nn
nn
n
nn
n
n
fa
Taylorseriesfxxa
n
x
xe
xn
xx
xx
nn
xx
xx
nn
x
x
n
¥
=
¥¥
==
+
¥¥
-
==
+
¥¥
==
¥
=
=-
==
-
+=-=-
+
=-=
+
=
å
åå
åå
åå
å
