## Transcribed Text

Question
tilhat is: Sintcos-l(x))
$ 1-*
B)ffi
C) 1-x
L
D)-
Qus$st 4
Evaluat€ the sum: f n(a + f)
n*L
A) 10
B) 18
c) 20
D) 40
Question 5
Apply substitution : x=6'tan(0)
1
to simplify an expression ffi
v5 A) ;;"r-(e)
B) 5'Cos{0}
L
C)
=
Cos(o) vf, o)#
12
10
A)
B)
c)
D)
Question 2
A 6 pound object stretches a spring 3 inches'
How much work is required to stretch this
spring from 3 to 5 inches?
L6
Question 6
Rewrite sum using sigma notation
sta*ins with k = 1'
-|+; -; - t
n) xLr?
el Etr#
c) Xtr(*l)n#
D) XEr(-Dn*
Question 3
Find derivative of arc tan (rff)
1 A)- ' !+xt
1 B)- ' 1-+xc
1, ta\ *
"t 2.fi7t+x1
x D)- ' 1-+xz
Question 7
Find all values of x for which the given
geometric series convefges:
f r,, -:t- L\z )
k=1
0(x(1"
2<x<5
L<x<3
0<x<3
A)
B)
c)
D)
I
Question s
I
Find nartial sum Sa for the foltowing series:
lo
x'*#)
A)2
B)1
c)0
D)1,2
I
Question s
I t, tni, sequence converges or diverges:
I
l{#}
A) converges
B) diverges
C) neither
que$tion 10
Calculate the value of total sum for the
following infinite series:
111 1+-+-+-+... 4 t6 64'
!
3
2
:
4
3
A)
B)
c)
D)
See next page
Quesfon 11
Evaluate the integral:
fx2
J.;.rya*
Question 12
A rylindrical tank with radius 3 feet and height I feet is filled completely with a water
How much work it will take to pump all of the water over the top edge of the tank?
Specific Aravity of water is 62 poundslft3.
Question 13
Evaluate the integral:
r dx- tJ x2+ 2x*10
Question tlt
Apply integration by part:
f
I xzCos(x)dx
J
Question 15
Use partial fractions decomposition to find the integral:
rSxz+x*L2 t- J x3 +4x
Question 16
Evaluate the integral:
1t
r
I Coss(7r) dr
J
0
See next page
Question 17
Use the Ratio Te$t to determine if the series absolutely convergent:
6
s-r 22 )- /-t n!
}'.=t
que$tion 18
Calculate the Taylor polynomial (first three terms only) for the function f{x} * ln(x)
at th€ poilt c ='2.
Question 19
Find a bound for the'errof of apprsximation function f(x) = Cox(x) with polynomial Pl{x)
on interual l-r$12, N121. (See example 3 in section 10.11, page 4)
qu€ctioa 20
tlow many terms of Taylor series are needed to apptoximate f(x) = gI
within 0.001 on interval [0, 2I.

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